a note on a deterministic global optimization algorithm abstract in this technical note we give a short extension application for a deterministic global optimization algorithm proposed in y ji k c zhang s j qu a deterministic global optimization algorithm applied mathematics and computation 185 2007 382 387 actually our result is slightly more general since it does not impose any special sign restrictions on numerators and denominators of the ratios the only assumption is that the denominators of the ratios are nonzero over the feasible region of the problem for clarity we use the same notations for the different equivalent problems and the corresponding relaxation linear programming rlp as done in ji et al 2007

a new l curve for ill posed problems the truncated singular value decomposition is a popular method for the solution of linear ill posed problems the method requires the choice of a truncation index which affects the quality of the computed approximate solution this paper proposes that an l curve which is determined by how well the given data right hand side can be approximated by a linear combination of the first few left singular vectors or functions be used as an aid for determining the truncation index

a deterministic global optimization algorithm in this paper we consider a deterministic global optimization algorithm for solving a general linear sum of ratios lfp first an equivalent optimization problem lfp1 of lfp is derived by exploiting the characteristics of the constraints of lfp by a new linearizing method the linearization relaxation function of the objective function of lfp1 is derived then the linear relaxation programming rlp of lfp1 is constructed and the proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objection function and the solutions of a series of rlp and finally the numerical experiments are given to illustrate the feasibility of the proposed algorithm

a mathematical formulation for reactive transport that eliminates mineral concentrations we present a concise and general mathematical formulation for reactive transport in groundwater for general applications by means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules we present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods the sequential iteration approach sia and the direct substitution approach dsa our conclusion is that the proposed reduction of the number of variables is of special interest for the dsa we have applied one of these formulations to an example of the flushing of saline water by fresh water

a global strategy for solving reactive transport equations reactive transport models are complex nonlinear partial differential algebraic equations pdae coupling the transport engine with the geochemical operator we propose an efficient and robust global numerical method based on a method of lines and differential algebraic equations dae solvers combined with a newton method using a powerful sparse linear solver numerical experiments show the performances of the method we also propose a unified framework to describe classical methods such as sequential non iterative approach sequential iterative approach direct substitution approach and compare them with our global method

an fptas for optimizing a class of low rank functions over a polytope we present a fully polynomial time approximation scheme fptas for optimizing a very general class of non linear functions of low rank over a polytope our approximation scheme relies on constructing an approximate pareto optimal front of the linear functions which constitute the given low rank function in contrast to existing results in the literature our approximation scheme does not require the assumption of quasi concavity on the objective function for the special case of quasi concave function minimization we give an alternative fptas which always returns a solution which is an extreme point of the polytope our technique can also be used to obtain an fptas for combinatorial optimization problems with non linear objective functions for example when the objective is a product of a fixed number of linear functions we also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor unless p np we prove this by showing a similar hardness of approximation result for supermodular function minimization a result that may be of independent interest

a four russians algorithm for regular expression pattern matching given a regular expression r of length p and a word a of length n the membership problem is to determine if a is in the language denoted by r an o pn lg n time algorithm is presented that is based on a lg n speedup of the standard o pn time simulation of r s nonderministic finite automaton on a using a combination of the node listing and four russians paradigms this result places a new worst case upper bound on regular expression pattern matching moreover in practice the method provides an implementation that is faster than existing software for small regular expressions

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

a new accelerating method for globally solving a class of nonconvex programming problems abstract in this paper we combine the new global optimization method proposed by jiao h jiao a branch and bound algorithm for globally solving a class of nonconvex programming problems nonlinear anal 70 2 2008 1113 1123 with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving a class of nonconvex programming problems np this technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of np does not exist and can be seen as an accelerating device for the global optimization algorithm of the nonconvex programming problems compared with the method in the above cited reference numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations the required list length and the overall execution time of the algorithm

a branch and bound algorithm for globally solving a class of nonconvex programming problems abstract a branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems np for minimizing the problem linear lower bounding functions llbfs of objective function and constraint functions are constructed then a relaxation linear programming is obtained which is solved by the simplex method and which provides the lower bound of the optimal value the proposed algorithm is convergent to the global minimum through the successive refinement of linear relaxation of the feasible region and the solutions of a series of linear programming problems and finally the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm

diffusive and chemotactic cellular migration smooth and discontinuous traveling wave solutions a mathematical model describing cell migration by diffusion and chemotaxis is considered the model is examined using phase plane numerical and perturbation techniques for a proliferative cell population travelingwave solutions are observed regardless of whether the migration is driven by diffusion chemotaxis or a combination of the two mechanisms for pure chemotactic migration both smooth and discontinuous solutions with shocks are shown to exist using phase plane analysis involving a curve of singularities and identical results are obtained numerically alternatively pure diffusive migration and combinations of diffusive and chemotactic migration yield smooth solutions only for all cases the wave speed depends on the exponential decay rate of the initial cell density and it is bounded by a minimum value which is numerically observed whenever the initial cell distribution has compact support the minimum wave speed c min is proportional to sqrt chi or sqrt d for pure chemotaxis

mm algorithms for geometric and signomial programming this paper derives new algorithms for signomial programming a generalization of geometric programming the algorithms are based on a generic principle for optimization called the mm algorithm in this setting one can apply the geometric arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated thus unconstrained signomial programming reduces to a sequence of one dimensional minimization problems simple examples demonstrate that the mm algorithm derived can converge to a boundary point or to one point of a continuum of minimum points conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming convergence to an interior point occurs at a linear rate finally the mm framework easily accommodates equality and inequality constraints of signomial type for the most important special case constrained quadratic programming the mm algorithm involves very simple updates

a practicable contraction approach for the sum of the generalized polynomial ratios problem abstract in this paper a practicable contraction approach is proposed for solving the sum of the generalized polynomial ratios problem p with generalized polynomial constraints due to the intrinsic difficulty of problem p less work has been devoted to solving this problem the proposed approach is based on reducing the original nonconvex problem p as a standard geometric programming gp problem by utilizing simple transformation and contraction strategies the resulting optimization problem can be solved effectively by utilizing the solutions of a series of gp problems the tractability and effectiveness of the proposed successive contraction approach are demonstrated by several numerical examples and the performance comparison of the proposed approach and other methods published is also presented in terms of solution quality

mathematical optimization ideas for biodiversity conservation several major environmental issues like biodiversity loss and climate change currently concern the international community these topics that are related to the development of human societies have become increasingly important since the united nations conference on environment and development unced or earth summit in rio de janeiro in 1992 in this article we are interested in the first issue we present here many examples of the help that using mathematical programming can provide to decision makers in the protection of biodiversity the examples we have chosen concern the selection of nature reserves the control of adverse effects caused by landscape fragmentation including the creation or restoration of biological corridors the ecological exploitation of forests the control of invasive species and the maintenance of genetic diversity most of the presented models are or can be approximated with linear quadratic or fractional integer formulations and emphasize spatial aspects of conservation planning many of them represent decisions taken in a static context but temporal dimension is also considered the problems presented are generally difficult combinatorial optimization problems some are well solved and others less well research is still needed to progress in solving them in order to deal with real instances satisfactorily moreover relations between researchers and practitioners have to be strengthened furthermore many recent achievements in the field of robust optimization could probably be successfully used for biodiversity protection a domain in which many data are uncertain

analysis of discontinuous galerkin methods for multicomponent reactive transport problems primal discontinuous galerkin dg methods including the oden babuska baumann version of dg are formulated for solving multicomponent reactive transport problems in porous media using the information of chemical stoichiometry an efficient approach is proposed for a special case of multicomponent reactive transport without immobile species a priori error analysis is conducted to establish the convergence of dg methods for multicomponent reactive transport systems which is optimal in h and nearly optimal in p

an efficient algorithm for globally solving generalized linear multiplicative programming generalized linear multiplicative programming problems are difficult problems known to be n p hard and they frequently arise in various areas such as engineering economics finance etc at present most of the global optimization algorithms for this kind of problems are mainly developed based on those kinds of branch and bound algorithms in this study a new algorithm based on the concept of level set is presented for globally solving generalized linear multiplicative programming problems the proposed algorithm is concise and easy to implement so it is quite suitable for engineering applications finally the global convergence is presented and the practical efficiency of the algorithm is demonstrated by the numerical experiments

numerical methods based on additive splittings for hyperbolic partial differential equations we derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds these techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales some of which are sometimes treated exactly the efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator this is analyzed and a technique is discussed for reducing this error through a simple change of variables a procedure for generating the appropriate boundary data for the intermediate solutions is also presented

mass balance errors when solving the convective form of the transport equation in transient flow problems 1 the original divergence form of the solute transport equation expresses the mass balance of solutes in groundwater the alternative convective form can be obtained by subtracting the flow equation multiplied by concentration from the original form many investigators prefer the latter because it facilitates the use of lagrangian or mixed eulerian lagrangian numerical methods for solution however it performs very poorly in transient contaminant transport problems with large temporal variations in water content we propose an alternative to overcome this difficulty it consists of evaluating the water content at time level k 1 if concentration in the convective term is evaluated at time level k for this reason we have called it reverse time weighting whereas we call an evaluation of the water content at time level k straight time weighting we show that reverse time weighting improves significantly over straight time weighting not only in terms of mass balance errors but also in terms of concentration errors

global optimization for sum of linear ratios problem with coefficients the global optimization of the sum of linear ratios problem has attracted the interest of researchers and practitioners for a number of years since these types of optimization problems are nonconvex various specialized algorithms have been proposed for globally solving these problems however these algorithms are only for the case that sum of linear ratios problem without coefficients and may be difficult to implement in this paper a branch and bound algorithm is proposed for globally solving the sum of linear ratios problem with coefficients by utilizing an equivalent problem and linearization technique the initial nonconvex programming problem is reduced to a sequence of linear programming problems the proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems numerical results are given to show the feasibility and effectiveness of the proposed algorithm

a simplicial branch and bound duality bounds algorithm for the linear sum of ratios problem in this article we present and validate a simplicial branch and bound duality bounds algorithm for globally solving the linear sum of ratios fractional program the algorithm computes the lower bounds called for during the branch and bound search by solving ordinary linear programming problems these problems are derived by using lagrangian duality theory the algorithm applies to a wide class of linear sum of ratios fractional programs two sample problems are solved and the potential practical and computational advantages of the algorithm are indicated

approximation of linear fractional multiplicative problems in this paper we propose a fully polynomial time approximation scheme for a class of optimization problems where the feasible region is a polyhedral one and the objective function is the sum or product of ratios of linear functions the class includes the well known ones of linear sum of ratios fractional programming and multiplicative programming

operator splitting for chemical reaction systems with fast chemistry abstract splitting methods are frequently used for large scale chemical reaction systems the main reason is the reduced computational cost for solving the subproblems in comparison to the time integration of the full problem however a splitting error is introduced the most popular splitting schemes are the first order lie trotter splitting and the second order strang splitting however in case of stiff differential equations the strang splitting suffers from order reduction and both schemes have order one for stiff differential equations therefore the step size restrictions due to the low order can result in a prohibitive small step size hence splitting schemes with order larger than one are necessary for stiff differential equations the richardson extrapolation of the lie trotter splitting is a second order scheme in this paper we examine differential equations with a fast chemical source term and a slow transport term thus all stiffness of the system is related to the chemical source term we show that the richardson extrapolation does not suffer from order reduction in this case furthermore we perform a stability analysis of the extrapolated splitting scheme for a linear test problem thereby the operators of the test problem do not commute

some matrix nearness problems suggested by tikhonov regularization abstract the numerical solution of linear discrete ill posed problems typically requires regularization i e replacement of the available ill conditioned problem by a nearby better conditioned one the most popular regularization methods for problems of small to moderate size are tikhonov regularization and truncated singular value decomposition tsvd by considering matrix nearness problems related to tikhonov regularization several novel regularization methods are derived these methods share properties with both tikhonov regularization and tsvd and can give approximate solutions of higher quality than either one of these methods

extension of tikhonov regularization method using linear fractional programming abstract this paper presents an extended form of the tikhonov regularization method this method is obtained by adding some parameters to the tikhonov regularization method the added parameters are obtained by solving a linear fractional programming problem finally some numerical examples are given to show the efficiency and validity of the new method

a note on the theoretical foundations of particle tracking methods in heterogeneous porous media 1 in this technical note the stochastic process for the path of particles undergoing convection dispersion in a heterogeneous media with sharp interfaces is derived the derived process is shown to correspond to the numerical particle tracking scheme introduced on a more heuristic basis by hoteit et al 2002 who validated the accuracy of their numerical method in controlled laboratory experiments specifically it is shown that in the direction transverse to the flow u y and across an interface where the diffusion coefficient is discontinuous the stochastic particle path t y t is given by a rescaled version of ito and mckean s 1963 skew brownian motion for a uniquely determined value of a that depends on the values of the diffusion coefficient at either side of the interface these results help supply a theoretical foundation that supports the numerical schemes and experimental findings of hoteit et al 2002

anisotropic and dynamic mesh adaptation for discontinuous galerkin methods applied to reactive transport mesh adaptation strategies are proposed for discontinuous galerkin methods applied to reactive transport problems with emphasis on dynamic and anisotropic adaptation they include an anisotropic mesh adaptation scheme and two isotropic methods using an l 2 l 2 norm error estimator and a hierarchic error indicator these dynamic mesh adaptation approaches are investigated using benchmark cases numerical results demonstrate that the three approaches resolve time dependent transport adequately without slope limiting for both long term and short term simulations it is shown that these results apply to problems where either diffusion or advection dominates in different subdomains moreover for these schemes mass conservation is retained locally during dynamic mesh modification comparison studies indicate that the anisotropic mesh adaptation provides the most efficient meshes and has the least numerical diffusion among the three adaptation approaches 2005 elsevier b v all rights reserved

a global optimization algorithm for linear fractional programming in this paper we present an efficient branch and bound method for general linear fractional problem gfp first by using a transformation technique an equivalent problem ep of gfp is derived then by exploiting structure of ep a linear relaxation programming lrp of ep is obtained to implement the algorithm the main computation involve solving a sequence of linear programming problem which can be solved efficiently the proposed algorithm is convergent to the global maximum through the successive refinement of the solutions of a series of linear programming problems numerical experiments are reported to show the feasibility of our algorithm

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

computing non dominated solutions in molfp abstract in this paper we present a technique to compute the maximum of a weighted sum of the objective functions in multiple objective linear fractional programming molfp the basic idea of the technique is to divide by the approximate middle the non dominated region in two sub regions and to analyze each of them in order to discard one if it can be proved that the maximum of the weighted sum is in the other the process is repeated with the remaining region the process will end when the remaining regions are so little that the differences among their non dominated solutions are lower than a pre defined error through the discarded regions it is possible to extract conditions that establish weight indifference regions these conditions define the variation range of the weights that necessarily leads to the same non dominated solution an example illustrating the concept is presented some computational results indicating the performance of the technique are also presented

an operator splitting algorithm for coupled one dimensional advection diffusion reaction equations abstract an operator splitting algorithm for a system of one dimensional advection diffusion reaction equations describing the transport of non conservative pollutants is presented in this paper the algorithm is a strang type splitting procedure incorporating contributions from the inhomogeneous terms by the duhamel s principle the associated homogeneous equations are split into advection diffusion and reaction equations and solved by a backward method of characteristic a finite element method and an explicit runge kutta method respectively the boundary conditions applicable to the split equations are derived numerical analyses of the algorithm consisting of the stability the accuracy and the convergence of the solution procedure are presented the composite algorithm is second order accurate in time and space and conditionally stable the numerical characteristics of the algorithm are demonstrated by several examples

a modified tikhonov regularization method tikhonov regularization and truncated singular value decomposition tsvd are two elementary techniques for solving a least squares problem from a linear discrete ill posed problem based on these two techniques a modified regularization method is proposed which is applied to an arnoldi based hybrid method theoretical analysis and numerical examples are presented to illustrate the effectiveness of the method

a new numerical reduction scheme for fully coupled multicomponent transport reaction problems in porous media 1 a new systematic approach for the efficient computation of the transport and reaction of a multispecies multireaction system is developed the objective of this approach is to reduce the number of coupled nonlinear differential equations drastically while splitting errors are avoided the reduction mechanism is able to handle both kinetic reactions and heterogeneous equilibrium reactions and mobile and immobile species it leads to a formulation of the nonlinear system with a jacobian that has very few nonzero entries applications of the reduction mechanism to reaction networks including a biodegradation problem which is modeled by the monod approach are given two numerical examples demonstrate the speed up of the presented reduction mechanism

range division and linearization algorithm for a class of linear ratios optimization problems abstract this article interprets a range division and linearization algorithm for solving a class of fractional programming problems p with the sum or product of linear ratios objective function in the algorithm by dividing the outer space with respect to problem p into many polynomial rectangles the original non convex problem p is transformed and decomposed into a sequence of linear programming problems in order to improve the computational efficiency of the algorithm a new accelerating technique is introduced which deletes a large part of region of the outer space in which there exists no the optimal solution of p moreover the global convergence of the proposed algorithm is outlined and the computational complexity of it is investigated to demonstrate that it is a fully polynomial time approximation scheme finally the numerical computational results illustrate the feasibility and efficiency of the proposed algorithm

global optimization for sum of generalized fractional functions this paper considers the solution of generalized fractional programming gfp problem which contains various variants such as a sum or product of a finite number of ratios of linear functions polynomial fractional programming generalized geometric programming etc over a polytope for such problems we present an efficient unified method in this method by utilizing a transformation and a two part linearization method a sequence of linear programming relaxations of the initial nonconvex programming problem are derived which are embedded in a branch and bound algorithm numerical results are given to show the feasibility and effectiveness of the proposed algorithm

a note on taylor series approach to fuzzy multiple objective linear fractional programming abstract toksari in his paper taylor series approach to fuzzy multiobjective linear fractional programming published in information sciences 178 2008 proposed a new method to solve multiple objective linear fractional programming problems and declared that it is more effective when compare to previous methods he constructed fuzzy goals and then used first order taylor polynomials to approximate the corresponding linear fractional membership functions by linear functions aggregating the linear functions toksari obtained a crisp linear programming problem and claimed that it is equal to the fuzzy fractional one in this paper we indicate the fallacy that arises by using taylor approximation and propose an improved method that guarantees the efficiency of the solution it provides both practical applications from toksari s paper are recalled to show that the improvements we suggest are effective

fractional programming applications and algorithms abstract the paper deals with decision problems that give rise to the optimization of ratios subject to constraints these so called fractional programs have been treated in a considerable number of papers it is attempted to survey applications as well as solution methods in linear quadratic and concave convex fractional programming in the first part we give a detailed outline on the major areas of applications of fractional programming following a brief review on some basic theoretical results like duality relations in the second part we then discuss different algorithmic approaches a primal a dual and a parametric solution method is considered here we try to determine for each method the kind of fractional programs that are solved by it suitably

a branch and bound algorithm to globally solve the sum of several linear ratios in this paper we propose a branch and bound algorithm to globally solve the sum of several linear fractional functions over a polytope for minimizing problem a linear lower bounding function llbf of the objective function is constructed then a linear programming is obtained which is solved by a simplex algorithm and provides the lower bounding of the optimal value the proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems the numerical experiment is reported to show the effectiveness and feasibility of the proposed algorithm also this method is extended to solve the maximizing problems

a global optimization using linear relaxation for generalized geometric programming many local optimal solution methods have been developed for solving generalized geometric programming ggp but up to now less work has been devoted to solving global optimization of ggp problem due to the inherent difficulty this paper considers the global minimum of ggp problems by utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of ggp on a microcomputer

solving the sum of ratios problems by a harmony search algorithm the sum of ratios problems have numerous applications in economy and engineering the sum of ratios problems are considered to be difficult as these functions are highly nonconvex and multimodal in this study we propose a harmony search algorithm for solving a sum of ratios problem numerical examples are also presented to demonstrate the effectiveness and robustness of the proposed method in all cases the solutions obtained using this method are superior to those obtained from other methods

online parameterized dictionary matching with one gap abstract we study the online parameterized dictionary matching with one gap problem pdmog which is the following preprocess a dictionary d of d patterns where each pattern contains a special gap symbol that can match any string so that given a text t arriving online a character at a time we can report all the patterns from d that parameterized match to suffixes of the text that has arrived so far before the next character arrives two equal length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection the gap symbols are associated with bounds determining the possible lengths of matching strings online dictionary matching with one gap dmog captures the difficulty in a bottleneck procedure for cyber security as many digital signatures of viruses manifest themselves as patterns with a single gap parameterized match captures possible encryption of the patterns we also define the strict pdmog problem in which subpatterns of the same dictionary pattern should be parameterized matched via the same bijection this captures situations where subpatterns of a dictionary pattern are encoded simultaneously we study this problem for special case called alphabet saturated dictionairy where every subpattern contains all characters of the dictionary alphabet we use the following parameters to describe our results d is the total size of the dictionary not including the gaps plsc is the longest parameterized suffix chain of subpatterns in d op is the number of parameterized patterns occurrences in t and are the minimum left and maximum right gap borders in the non uniformly bounded dictionary case g d is the degeneracy of the graph g d representing dictionary d this graph is classified as sparse or dense according the value of the g d and plsc parameters we obtain o d preprocessing time space and o g d plsc plsc max m o p query time per text character algorithm for online pdmog with sparse graph dictionaries o d d preprocessing time space and o plsc d plsc max m o p query time per text character algorithm for online pdmog with dense graph dictionaries o d preprocessing time space and o g d plsc o p query time per text character algorithm for strict pdmog with alphabet saturated dictionaries these results are parallel to the ones obtained for the dictionary with one gap dmog problem almost matching the lower bounds achieved for this problem 7 while the parameter g d can be as large as d and much lager if the dictionary has non uniform gap boundaries and the parameter plsc could theoretically be as large as d in many practical situations these parameters are actually small the strength of our work is in achieving results that explore and exploit small values for these parameters thus supplying algorithms that are suitable for some practical cyber security needs

string matching with variable length gaps we consider string matching with variable length gaps given a string t and a pattern p consisting of strings separated by variable length gaps arbitrary strings of length in a specified range the problem is to find all ending positions of substrings in t that match p this problem is a basic primitive in computational biology applications let m and n be the lengths of p and t respectively and let k be the number of strings in p we present a new algorithm achieving time o email protected and space o m a where a is the sum of the lower bounds of the lengths of the gaps in p and a is the total number of occurrences of the strings in p within t compared to the previous results this bound essentially achieves the best known time and space complexities simultaneously consequently our algorithm obtains the best known bounds for almost all combinations of m n k a and a our algorithm is surprisingly simple and straightforward to implement we also present algorithms for finding and encoding the positions of all strings in p for every match of the pattern

a milp formulation for generalized geometric programming using piecewise linear approximations abstract generalized geometric programming ggp problems are converted to mixed integer linear programming milp problems using piecewise linear approximations our approach is to approximate a multiple term log sum function of the form log x 1 x 2 x n in terms of a set of linear equalities or inequalities of log x 1 log x 2 and log x n where x 1 x n are strictly positive the advantage of this approach is its simplicity and readiness to implement and solve using commercial milp solvers while milp problems in general are no easier than ggp problems this approach is justified by the phenomenal progress of computing power of both personal computers and commercial milp solvers the limitation of this approach is discussed along with numerical tests

a branch and cut algorithm for a class of sum of ratios problems the problem of maximizing a sum of concave convex ratios over a convex set is addressed the projection of the problem onto the image space of the functions that describe the ratios leads to the equivalent problem of maximizing a sum of elementary ratios subject to a linear semi infinite inequality constraint a global optimization algorithm that integrates a branch and bound procedure for dealing with nonconcavities in the image space and an efficient relaxation procedure for handling the semi infinite constraint is proposed and illustrated through numerical examples comparative computational analyses between the proposed algorithm and two alternative algorithms for solving sum of ratios problems are also presented

linear time computation of prefix table for weighted strings applications the prefix table of a string is one of the most fundamental data structures of algorithms on strings it determines the longest factor at each position of the string that matches a prefix of the string it can be computed in time linear with respect to the size of the string and hence it can be used efficiently for locating patterns or for regularity searching in strings a weighted string is a string in which a set of letters may occur at each position with respective occurrence probabilities weighted strings also known as position weight matrices or uncertain strings naturally arise in many biological contexts for example they provide a method to realise approximation among occurrences of the same dna segment in this article given a weighted string x of length n and a constant cumulative weight threshold 1 z defined as the minimal probability of occurrence of factors in x we present an o n time algorithm for computing the prefix table of x furthermore we outline a number of applications of this result for solving various problems on non standard strings and present some preliminary experimental results

an efficient algorithm for globally minimizing sum of quadratic ratios problem with nonconvex quadratic constraints in this paper a new branch and bound algorithm based on the rectangular partition and the lagrangian relaxation for solving sum of quadratic ratios problem with nonconvex quadratic constraints qsrp is proposed firstly the problem qsrp is converted into an equivalent sum of linear ratios problem with quadratic constraints lsrp then the bounding procedure is investigated by minimizing the restricted lagrangian function of lsrp with a given estimate of the lagrange multipliers minimizing a linear relaxation of the restricted lagrangian overcomes the difficulty that the restricted lagrangian is often nonconvex and facilitates the use of lagrangian duality within a global optimization framework in the algorithm the interval newton method is used to facilitate convergence in the neighborhood of the global solution the proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems finally numerical experiments are reported to show the efficiency of our algorithm

an outcome space finite algorithm for solving linear multiplicative programming this paper presents an outcome space finite algorithm for solving linear multiplicative programming in each iteration of which a convex quadratic programming is only solved in the paper we give a global optimization condition on a class of multiplicative programming problems and prove that the proposed algorithm is finite terminative and gain a global optimal solution of the former problem when it stops it can be shown by the numerical results that the proposed algorithm is effective and the computational results can be gained in short time

a reduction scheme for coupled multicomponent transport reaction problems in porous media generalization to problems with heterogeneous equilibrium reactions 1 in this article a systematic approach for the efficient computation of the transport and reaction of a multispecies multireaction system is proposed the objective of this approach is to reformulate the given system of differential or differential algebraic equations in such a way that the couplings and the nonlinearities are concentrated in a reduced number of equations if compared to the original formulation while some linear equations decouple from the system the resulting system is handled in the spirit of a global implicit approach one step method avoiding operator splitting techniques the reduction of the problem size proposed in this article helps to limit the large computational costs of numerical simulations for such problems the reduction mechanism is a generalization of the method proposed in a previous paper now problems with mixed mobile immobile species homogeneous heterogeneous kinetic equilibrium reactions are considered while the previous publication was restricted to problems without heterogeneous equilibrium reactions such as equilibrium sorption an application of the reduction mechanism to an example problem is given in order to investigate the reduction of the number of coupled nonlinear equations and to compare it to other methods

a new variant of l curve for tikhonov regularization in this paper we introduce a new variant of l curve to estimate the tikhonov regularization parameter for the regularization of discrete ill posed problems this method uses the solution norm versus the regularization parameter the numerical efficiency of this new method is also discussed by considering some test problems

accuracy of operator splitting for advection dispersion reaction problems an operator splitting approach is often used for the numerical solution of advection dispersion reaction problems operationally this approach advances the solution over a single time step in two stages one involving the solution of the nonreactive advection dispersion equation and the other the solution of the reaction equations the first stage is usually solved with a finite difference finite element or related technique while the second stage is normally solved with an ordinary differential equation integrator the only generally published guidelines on numerical accuracy suggest that the discretization errors associated with each stage must be small in order to achieve high accuracy of the overall solution however in this note we demonstrate that there is an inherent mass balance error present in the operator splitting algorithm for problems involving continuous mass influx boundary conditions the mass balance error does not exist for instantaneous mass input problems these conclusions are based upon analysis of a simple first order decay problem for which each stage of the calculation can be performed analytically i e without discretization error for this linear decay problem we find that the product of the first order decay coefficient k times t must be less than approximately 0 1 in order for the mass balance error to be less than 5 we also present a variant of the normal operator splitting algorithm in which the order of solving the advection dispersion and reaction operators is reversed at each time step this modification reduces the mass balance error by more than a factor of 10 for a wide range of k t values

a practicable branch and bound algorithm for sum of linear ratios problem abstract this article presents a practicable algorithm for globally solving sum of linear ratios problem slr the algorithm works by globally solving a bilinear programming problem eq that is equivalent to the problem slr in the algorithm by utilizing convex envelope and concave envelope of bilinear function the initial nonconvex programming problem is reduced to a sequence of linear relaxation programming problems in order to improve the computational efficiency of the algorithm a new accelerating technique is introduced which provides a theoretical possibility to delete a large part of the investigated region in which there exists no global optimal solution of the eq by combining this innovative technique with branch and bound operations a global optimization algorithm is designed for solving the problem slr finally numerical experimental results show the feasibility and efficiency of the proposed algorithm

strong duality for robust minimax fractional programming problems abstract we develop a duality theory for minimax fractional programming problems in the face of data uncertainty both in the objective and constraints following the framework of robust optimization we establish strong duality between the robust counterpart of an uncertain minimax convex concave fractional program termed as robust minimax fractional program and the optimistic counterpart of its uncertain conventional dual program called optimistic dual in the case of a robust minimax linear fractional program with scenario uncertainty in the numerator of the objective function we show that the optimistic dual is a simple linear program when the constraint uncertainty is expressed as bounded intervals we also show that the dual can be reformulated as a second order cone programming problem when the constraint uncertainty is given by ellipsoids in these cases the optimistic dual problems are computationally tractable and their solutions can be validated in polynomial time we further show that for robust minimax linear fractional programs with interval uncertainty the conventional dual of its robust counterpart and the optimistic dual are equivalent

global optimization of signomial geometric programming problems abstract this paper presents a global optimization approach for solving signomial geometric programming problems in most cases nonconvex optimization problems with signomial parts are difficult np hard problems to solve for global optimality but some transformation and convexification strategies can be used to convert the original signomial geometric programming problem into a series of standard geometric programming problems that can be solved to reach a global solution the tractability and effectiveness of the proposed successive convexification framework is demonstrated by seven numerical experiments some considerations are also presented to investigate the convergence properties of the algorithm and to give a performance comparison of our proposed approach and the current methods in terms of both computational efficiency and solution quality

global optimization of nonlinear sum of ratios problem this article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem p on nonconvex feasible region first a problem q is derived which is equivalent to problem p in the algorithm lower bounds are derived by solving a sequence of linear relaxation programming problems which is based on the construction of the linear lower bounding functions for the objective function and the constraint functions of the problem q over the feasible region the proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm

a global optimization algorithm for sum of quadratic ratios problem with coefficients abstract in this paper a global optimization algorithm for solving sum of quadratic ratios problem with coefficients and nonconvex quadratic function constraints nsp is proposed first the problem nsp is converted into an equivalent sum of linear ratios problem with nonconvex quadratic constraints lsp using a linearization technique the linearization relaxation problem of lsp is obtained the original problem is then solvable using the branch and bound method in the algorithm lower bounds are derived by solving a sequence of linear lower bounding functions for the objective function and the constraint functions of the problem nsp over the feasible region the proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems the numerical examples demonstrate that the proposed algorithm can easily be applied to solve problem nsp

global optimization of generalized linear fractional programming with nonlinear constraints this paper presents a branch and bound algorithm for globally solving a wide class of generalized linear fractional programming problems glfp this class includes such problems as minimizing a sum or error for product of a finite number of ratios of linear functions linear multiplicative programming polynomial programming etc over nonconvex feasible region first a problem q is derived which is equivalent to problem glfp in the algorithm lower bounds are derived by solving a sequence of linear relaxation programming problems which is based on the construction of the linear lower bounding functions for the objective function and constraint functions of problem q over the feasible region convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm

range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems many global optimization approaches for solving signomial geometric programming problems are based on transformation techniques and piecewise linear approximations of the inverse transformations since using numerous break points in the linearization process leads to a significant increase in the computational burden for solving the reformulated problem this study integrates the range reduction techniques in a global optimization algorithm for signomial geometric programming to improve computational efficiency in the proposed algorithm the non convex geometric programming problem is first converted into a convex mixed integer nonlinear programming problem by convexification and piecewise linearization techniques then an optimization based approach is used to reduce the range of each variable tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using fewer break points in the linearization process therefore decreasing the required cpu time several numerical experiments are presented to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality

solving sum of quadratic ratios fractional programs via monotonic function in this paper a branch reduce bound algorithm is proposed for globally solving a sum of quadratic ratios fractional programming with nonconvex quadratic constraints due to its intrinsic difficulty less work has been devoted to globally solving this problem the proposed algorithm is based on reformulating the problem as a monotonic optimization problem and it turns out that the optimal solution which is provided by the algorithm is adequately guaranteed to be feasible and to be close to the actual optimal solution convergence of the algorithm is shown and the numerical experiments are given to show the feasibility of the proposed algorithm

a hybrid pso ga algorithm for constrained optimization problems the main objective of this paper is to present a hybrid technique named as a pso ga for solving the constrained optimization problems in this algorithm particle swarm optimization pso operates in the direction of improving the vector while the genetic algorithm ga has been used for modifying the decision vectors using genetic operators the balance between the exploration and exploitation abilities have been further improved by incorporating the genetic operators namely crossover and mutation in pso algorithm the constraints defined in the problem are handled with the help of the parameter free penalty function the experimental results of constrained optimization problems are reported and compared with the typical approaches exist in the literature as shown the solutions obtained by the proposed approach are superior to those of existing best solutions reported in the literature furthermore experimental results indicate that the proposed approach may yield better solutions to engineering problems than those obtained by using current algorithms

an interior point method for generalized linear fractional programming we develop an interior point polynomial time algorithm for a generalized linear fractional problem the latter problem can be regarded as a nonpolyhedral extension of the usual linear fractional programming typical example which is of interest for control theory is the minimization of the generalized eigenvalue of a pair of symmetric matrices linearly depending on the decision variables

inventory model of deteriorated items with a constraint a geometric programming approach an inventory model for deteriorating items is built up with limited storage space here demand rate for the items is finite items deteriorate at constant rates and are replenished instantaneously following eoq model the problem is formulated with and without truncation on the deterioration term and ultimately is converted to the minimization of a signomial expression with a posynomial constraint it is solved by modified geometric programming mgp method and non linear programming nlp method the problem is supported by numerical examples the results from two versions of the model with and without truncation and two methods i e mgp and nlp are compared

on solving the sum of ratios problem this paper addresses the development of efficient global search methods for fractional programming problems such problems are in general nonconvex with numerous local extremums and belong to a class of global optimization problems first we reduce a rather general fractional programming problem with d c functions to solving an equation with a vector parameter that satisfies some nonnegativity assumption this theorem allows the justified use of the generalized dinkelbachs approach for solving fractional programming problems with a d c goal function based on solving of some d c minimization problem we developed a global search algorithm for fractional programming problems which was tested on a set of low dimensional test problems taken from the literature as well as on randomly generated problems with up to 200 variables or 200 terms in the sum

motif matching using gapped patterns we consider the problem of matching a set mathcal p of gapped patterns against a given text t of length n where a gapped pattern is a sequence of strings keywords over a finite alphabet of size such that there is a gap of fixed length between each two consecutive strings we assume the ram model with words of size w in bits we are interested in computing the list ofmatching patterns for each position in the text this problem is a specific instance of the variable length gaps problem 2 vlg problem for multiple patterns and has applications in the discovery of transcription factor tf binding sites in dna sequences when using generalized versions of the positionweightmatrix pwm model to representtf binding specificities the paper 5 describes howa motif represented as a generalizedpwm can bematched as a set of gapped patternswith unit length keywords and presents algorithms for the restricted case of patterns with two unit length keywords

a simplicial branch and duality bound algorithm for the sum of convex convex ratios problem this article presents a simplicial branch and duality bound algorithm for globally solving the sum of convex convex ratios problem with nonconvex feasible region to our knowledge little progress has been made for globally solving this problem so far the algorithm uses a branch and bound scheme where the lagrange duality theory is used to obtain the lower bounds as a result the lower bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently it has been proved that the algorithm possesses global convergence finally the numerical experiments are given to show the feasibility of the proposed algorithm

fast profile matching algorithms a survey position specific scoring matrices are a popular choice for modelling signals or motifs in biological sequences both in dna and protein contexts a lot of effort has been dedicated to the definition of suitable scores and thresholds for increasing the specificity of the model and the sensitivity of the search it is quite surprising that until very recently little attention has been paid to the actual process of finding the matches of the matrices in a set of sequences once the score and the threshold have been fixed in fact most profile matching tools still rely on a simple sliding window approach to scan the input sequences this can be a very time expensive routine when searching for hits of a large set of scoring matrices in a sequence database in this paper we will give a survey of proposed approaches to speed up profile matching based on statistical significance multipattern matching filtering indexing data structures matrix partitioning fast fourier transform and data compression these approaches improve the expected searching time of profile matching thus leading to implementation of faster tools in practice

modeling of chemically reactive groundwater transport a complete reactive groundwater transport model must account for both chemical and transport processes for the chemical processes one has to decide whether to formulate them kinetically or to assume a local chemical equilibrium state this decision in the chemical model part determines the mathematical structure of the overall model in a kinetic formulation the linear partial differential equations of the transport have to be coupled with a nonlinear system of ordinary differential equations describing the kinetic development whereas in an equilibrium formulation the equations of the transport are coupled to a nonlinear system of algebraic equations describing the equilibrium state basically two kinds of methods for solving reactive transport systems may be distinguished namely one step methods which simultaneously solve the transport and the chemical model parts and two step methods which solve these model parts separately we here present a sequential two step method for kinetic transport models and an iterative two step method for equilibrium transport models we conduct a timescale analysis to check whether the error of the sequential two step method is tolerable and whether a given kinetic transport system can be reduced to an equilibrium one the numerical methods and the timescale analysis are applied to two test cases zysset et al 1994 present a further application of the kinetic transport model to laboratory column experiments governed by biodegradation

high order multi implicit spectral deferred correction methods for problems of reactive flow models for reacting flow are typically based on advection diffusion reaction a d r partial differential equations many practical cases correspond to situations where the relevant time scales associated with each of the three sub processes can be widely different leading to disparate time step requirements for robust and accurate time integration in particular interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection the numerical strategy introduced in this paper is a general procedure to account for this time scale disparity the proposed methods are high order multi implicit generalizations of spectral deferred correction methods misdc methods constructed for the temporal integration of a d r equations spectral deferred correction methods compute a high order approximation to the solution of a differential equation by using a simple low order numerical method to solve a series of correction equations each of which increases the order of accuracy of the approximation the key feature of misdc methods is their flexibility in handling several sub processes implicitly but independently while avoiding the splitting errors present in traditional operator splitting methods and also allowing for different time steps for each process the stability accuracy and efficiency of misdc methods are first analyzed using a linear model problem and the results are compared to semi implicit spectral deferred correction methods furthermore numerical tests on simplified reacting flows demonstrate the expected convergence rates for misdc methods of orders three four and five the gain in efficiency by independently controlling the sub process time steps is illustrated for nonlinear problems where reaction and diffusion are much stiffer than advection although the paper focuses on this specific time scales ordering the generalization to any ordering combination is straightforward

an investigation of eulerian lagrangian methods for solving heterogeneous advection dominated transport problems numerical simulation of solute transport in heterogeneous porous media is greatly complicated by the large velocity and concentration gradients induced by spatial variations in hydraulic conductivity eulerian lagrangian methods for solving the transport equation can give accurate solutions to heterogeneous problems if their interpolation algorithms are properly selected this paper compares the performance of four eulerian lagrangian solvers that rely on linear quadratic cubic spline and taut spline interpolators in each case a tensor product decomposition is used to reduce the general n dimensional interpolation problem to a sequence of n one dimensional problems comparisons of a set of test problems indicate that the linear and taut spline interpolators are dispersive while the quadratic and cubic spline interpolators are oscillatory the cubic and taut spline interpolators give consistently better accuracy than the more conventional linear and quadratic alternatives simulation experiments in two and three dimensional heterogeneous media indicate that the taut spline interpolator which is applied here for the first time to a solute transport problem is able to yield accurate essentially nonoscillatory solutions for high grid peclet numbers the cubic spline interpolator requires significantly less computational effort to achieve performance comparable to the other methods