recognition problems for special classes of polynomials in 0 1 variables this paper investigates the complexity of various recognition problems for pseudo boolean functions i e real valued functions defined on the unit hypercubebn 0 1 n when such functions are represented as multilinear polynomials in their variables determining whether a pseudo boolean function a is monotonic or b is supermodular or c is threshold or d has a unique local maximum in each face ofbn or e has a unique local maximum inbn is shown to be np hard a polynomial time recognition algorithm is presented for unimodular functions previously introduced by hansen and simeone as a class of functions whose maximization overbn is reducible to a network minimum cut problem

a computational method for finding all the roots of a vector function based on dynamical systems theory a computational method is proposed to locate all the roots of a nonlinear vector function the computational approach utilizes the cell mapping method this method relies on discretization of the state space and is a convenient and powerful numerical tool for analyzing the global behavior of nonlinear systems our study shows that it is efficient and effective for determining roots because it minimizes and simplifies computations of system trajectories since the roots are asymptotically stable equilibrium points of the autonomous dynamical system it also provides the domains of attraction associated with each root other numerical techniques based on iterative and homotopic methods can make use of these domains to choose appropriate initial guesses singular manifolds play an important role in limiting the extent of these domains of attraction both a theoretical basis and a computational algorithm for locating the singular manifolds are also provided they make use of similar state space discretization frameworks examples are given to illustrate the computational approaches it is demonstrated that for one of the examples a mechanical system the method yields many more solutions than those previously reported

lipschitz continuity of triangular subnorms this paper deals with the lipschitz property of triangular subnorms unlike the case of triangular norms for these operations the problem is still open and presents an interesting variety of situations we provide some characterization results by weakening the notion of convexity introducing two generalized versions of convexity for real functions called a lower convexity and sub convexity the a lower convex and sub convex real mappings present characteristics quite different from the usual convex real mappings we will discuss the link between such kind of functions and the generators and their pseudo inverse of continuous archimedean triangular subnorms

p quasihyponormal operators have scalar extensions of order 6 abstract in this paper we show that every p quasihyponormal operator has a scalar extension of order 6 i e is similar to the restriction to a closed invariant subspace of a scalar operator of order 6 where 0 p 1 as a corollary we get that every p quasihyponormal operator with rich spectra has a nontrivial invariant subspace also we show that aluthge transforms preserve an analogue of the single valued extension property for w 2 d h and an operator t

empirical evaluation of innovations in interval branch and bound algorithms for nonlinear systems interval branch and bound algorithms for finding all roots use a combination of a computational existence uniqueness procedure and a tessellation process generalized bisection such algorithms identify with mathematical rigor a set of boxes that contains unique roots and a second set within which all remaining roots must lie though each root is contained in a box in one of the sets the second set may have several boxes in clusters near a single root thus the output is of higher quality if there are relatively more boxes in the first set in contrast to previously implemented similar techniques a box expansion technique in this paper based on using an approximate root finder epsilon inflation and exact set complementation decreases the size of the second set increases the size of the first set and never loses roots in addition to the expansion technique use of second order extensions to eliminate small boxes that do not contain roots and interval slopes versus interval derivative matrices are studied these items are evaluated empirically on a significant test problem set within a fortran 90 environment designed for such purposes the results are compared with previous results and show that careful incorporation of the techniques yields both quantitatively and qualitatively superior computer codes

solving a huff like competitive location and design model for profit maximization in the plane abstract a chain wants to set up a single new facility in a planar market where similar facilities of competitors and possibly of its own chain are already present fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility determined by the different perceived qualities of the facilities and the distances to them through a gravitational or logit type model both the location and the quality design of the new facility are to be found so as to maximise the profit obtained for the chain several types of constraints and costs are considered two solution methods are developed and tested the first is a repeated local optimisation heuristic extending earlier proposals to the supplementary design question and the presence of locational constraints the second is an exact global optimisation technique based on reliable computing using interval analysis incorporating several novel features an example and comparative computational results demonstrate that this difficult and very multi modal problem can be solved by such techniques the local optimisation method turns out not to be very robust in its results even after numerous repetitions whereas the global optimisation method yields very useful and complete information on guaranteed near to optimal solutions after an important but still quite acceptable computational effort

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

isolated points of spectrum of p k quasihyponormal operators let t be a p k quasihyponormal operator on a complex hilbert space i e t k t t p tt p tk 0 for a positive number 0 p 1 and a positive integer k let 0 be an isolated point of t and e the riesz idempotent for 0 in this paper we prove that 1 if 0 0 then e is self adjoint and eh ker t 0 ker t 0 2 if 0 0 then eh ker tk

validated linear relaxations and preprocessing some experiments based on work originating in the early 1970s a number of recent global optimization algorithms have relied on replacing an original nonconvex nonlinear program by convex or linear relaxations such linear relaxations can be generated automatically through an automatic differentiation process this process decomposes the objective and constraints if any into convex and nonconvex unary and binary operations the convex operations can be approximated arbitrarily well by appending additional constraints while the domain must somehow be subdivided in an overall branch and bound process or in some other local process to handle nonconvex constraints in general a problem can be hard if even a single nonconvex term appears however certain nonconvex terms lead to easier to solve problems than others recently neumaier lebbah michel ourselves and others have paved the way to utilizing such techniques in a validated context in this paper we present a symbolic preprocessing step that provides a measure

nonlinear optimization exclusion tests for finding all solutions of nonlinear equations abstract exclusion tests are a well known tool in the area of interval analysis for finding the zeros of a function over a compact domain recently k georg developed linear programming exclusion tests based on taylor expansions in this paper we modify his approach by choosing another objective function and using nonlinear constraints to make the new algorithm converges faster than the algorithm in k georg a new exclusion test j comput appl math 152 2003 147 160 in this way we reduce the number of subinterval in each level the computational complexity for the new tests are investigated also numerical results and comparisons will be presented

a new augmented singular transform and its partial newton correction method for finding more solutions to nonvariational quasilinear elliptic pdes abstract in this paper in order to find more solutions to a nonvariational quasilinear pde a new augmented singular transform ast is developed to form a barrier surrounding previously found solutions so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found solution thus a solution found by the algorithm must be new mathematical justifications of ast formulation are established a partial newton correction method is designed accordingly to solve the augmented problem and to satisfy a constraint in ast the new method is applied to numerically investigate bifurcation symmetry breaking phenomena to a non variational quasilinear elliptic equation through finding multiple solutions such phenomena are numerically captured and visualized for the first time and still open for theoretical verification since the formulation is general and simple it opens a door to solve other multiple solution problems

on operators satisfying t t2 t t t 2t abstract let t be a bounded linear operator on a complex hilbert space h in this paper we introduce the class denoted qa of operators satisfying t t 2 t t t 2 t and we prove basic structural properties of these operators using these results we also prove that if e is the riesz idempotent for a non zero isolated point of the spectrum of t qa then e is self adjoint and we give a necessary and sufficient condition for t s to be in qa when t and s are both non zero operators

on continuous triangular norms the problem of converging to any given continuous triangular norm by a sequence of continuous archimedean triangular norms is studied such a sequence is built up in a constructive way the class of well founded triangular norms is introduced it is proved that a sequence of triangular norms converges to a given continuous triangular norm if and only if this convergence is uniform finally we prove that every continuous triangular norm is a uniform limit of continuous archimedean triangular norms

convergence of residuated operators and connective stability of non classical logics some of the results of jenei 1993 are put in a more general setting in this paper the convergence of the residuated connectives related to a sequence of left continuous triangular norms to the residuated connective of the limit triangular norm is studied two sufficient and necessary conditions are given a derived concept the connective stability of non classical logics is introduced and investigated it is established that godel s logic some girard s logics and further non classical logics are connective stable

an efficient and safe framework for solving optimization problems interval methods have shown their ability to locate and prove the existence of a global optima in a safe and rigorous way unfortunately these methods are rather slow efficient solvers for optimization problems are based on linear relaxations however the latter are unsafe and thus may overestimate or worst underestimate the very global minima this paper introduces quadopt an efficient and safe framework to rigorously bound the global optima as well as its location quadopt uses consistency techniques to speed up the initial convergence of the interval narrowing algorithms a lower bound is computed on a linear relaxation of the constraint system and the objective function all these computations are based on a safe and rigorous implementation of linear programming techniques first experimental results are very promising

preconditioners for the interval gauss seidel method interval newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box bf x subset bf r n of a system of nonlinear equations f x 0 with mathematical certainty even in finite precision arithmetic in such methods the system f x 0 is transformed into a linear interval system 0 f m bf f bf x bf bar x m if interval arithmetic is then used to bound the solutions of this system the resulting box bf bar x contains all roots of the nonlinear system the interval gauss seidel method is a reasonable way of finding such solution bounds for the overall interval newton bisection algorithm to be efficient the image box bf bar x should be as small as possible to do this the linear interval system is multiplied by a preconditioner matrix y before the interval gauss seidel method is applied in this paper a technique for computing such preconditioner matrices y is described this te

a branch and cut algorithm for nonconvex quadratically constrained quadratic programming we present a branch and cut algorithm that yields in finite time a globally e optimal solution with respect to feasibility and optimality of the nonconvex quadratically constrained quadratic programming problem the idea is to estimate all quadratic terms by successive linearizations within a branching tree using reformulation linearization techniques rlt to do so four classes of linearizations cuts depending on one to three parameters are detailed for each class we show how to select the best member with respect to a precise criterion the cuts introduced at any node of the tree are valid in the whole tree and not only within the subtree rooted at that node in order to enhance the computational speed the structure created at any node of the tree is flexible enough to be used at other nodes computational results are reported that include standard test problems taken from the literature some of these problems are solved for the first time with a proof of global optimality

solving polynomial systems using a branch and prune approach this paper presents tt newton a branch and prune algorithm used to find all isolated solutions of a system of polynomial constraints tt newton can be characterized as a global search method which uses intervals for numerical correctness and for pruning the search space early the pruning in tt newton consists of enforcing at each node of the search tree a unique local consistency condition called box consistency which approximates the notion of arc consistency well known in artificial intelligence box consistency is parametrized by an interval extension of the constraint and can be instantiated to produce the hansen sengupta narrowing operator used in interval methods as well as new operators which are more effective when the computation is far from a solution tt newton has been evaluated on a variety of benchmarks from kinematics chemistry combustion economics and mechanics on these benchmarks it outperforms the interval methods we are aware of and compares well with textit state of the art continuation methods limitations of tt newton e g a sensitivity to the size of the initial intervals on some problems are also discussed of particular interest is the mathematical and programming simplicity of the method

safe bounds in linear and mixed integer linear programming current mixed integer linear programming solvers are based on linear programming routines that use floating point arithmetic occasionally this leads to wrong solutions even for problems where all coefficients and all solution components are small integers an example is given where many state of the art milp solvers fail it is then shown how using directed rounding and interval arithmetic cheap pre and postprocessing of the linear programs arising in a branch and cut framework can guarantee that no solution is lost at least for mixed integer programs in which all variables can be bounded rigorously by bounds of reasonable size

on an application of dynamical systems theory to determine all the zeros of a vector function abstract a continuous time dynamical system is constructed and analyzed in this paper to help locate all the zeros of nonlinear vector functions lyapunov stability technique is used to show that the zeros of the vector function become asymptotically stable equilibria for this dynamical system a strict lyapunov function is constructed to indicate local stability and to estimate the domains of attraction of all equilibria manifolds on which the jacobian of the vector field is singular play a significant role in characterizing the global behavior of the system examples are provided to illustrate the extent of the theory new computational techniques to determine all the zeros of a vector function can be developed based on the dynamical aspects of the theory given in this paper

existence test for solution of nonlinear systems applying affine arithmetic a computational test is proposed for existence of solution in nonlinear systems in this test an interval inclusion of newton mapping is estimated applying affine arithmetic numerical examples are presented to show the efficiency of this test

finding all solution sets of piecewise linear interval equations using an integer programming solver abstract this paper presents an efficient and easily implementable method for finding all solution sets of piecewise linear interval equations using integer programming in this method the problem of finding all solution sets is formulated as a mixed integer programming problem and it is solved by a high performance integer programming solver such as cplex it is shown that all solution sets are obtained by solving a single mixed integer programming problem and related linear programming problems numerical examples are given to confirm the effectiveness of the proposed method

a new exclusion test exclusion tests are a well known tool for obtaining all solutions of a nonlinear system of equations see e g the work of krawczyk or moore recently yamamura and collaborators have developed linear programming exclusion tests that turned out to be highly successful for nonlinear problems in electrical networking the author has developed higher order exclusion tests based on taylor expansions in the present paper it is shown that the ideas behind both approaches can be combined we present a new class of higher order linear programming exclusion tests investigate their computational complexity and illustrate their performance on several examples

some results on the degree of symmetry of fuzzy relations abstract in this paper we investigate the degree of the symmetry of fuzzy relations on a set x based on the fuzzy e equality derived from uninorms with unit element e the degree of the symmetry of fuzzy relations are defined by two different approaches the type i degree of symmetry and the type ii degree of symmetry the main work of this paper include first we discuss some basic properties of those two degrees especially for the relationship between them in particular for continuous t norms we give a necessary and sufficient condition such that the type i degree of symmetry and the type ii degree of symmetry are equal and then we obtain that the type ii degree of symmetry is more appropriate to character the degree of the symmetry of fuzzy relations than the type i degree of symmetry with respect to whether they preserve the fuzzy e equalities or not in the meantime for a special case with continuous t norms we provide a necessary and sufficient condition such that the type i degree of symmetry preserves the fuzzy equalities finally for conjunctive left continuous idempotent uninorms with neutral element e 0 1 we find out a symmetric fuzzy relation s which is close enough to the given fuzzy relation r with respect to fuzzy e equality such that the degree of fuzzy e equality of s and r is the type ii degree of symmetry of r in particular we obtain analogous results for continuous t norms and one class of left continuous t norms

finding all solutions of nonlinear equations using the dual simplex method recently an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming this algorithm is based on a simple test termed the lp test for nonexistence of a solution to a system of nonlinear equations using the dual simplex method in this letter an improved version of the lp test algorithm is proposed by numerical examples it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time

idempotent integral as limit of g integrals we show that sup and inf decomposable measures can be obtained as limits of families of pseudo additive measures with respect to generated pseudo additions the corresponding integrals with respect to sup or inf decomposable measures can be obtained as limits of families of g integrals

a general cdc formulation for specializing the cell exclusion algorithms of finding all zeros of vector functions let j be the family of analytic compositions of analytic mappings and their absolute values a novel inequality on the range of the mappings in j is proved which is then used to yield a universal cdc cell discarded condition formulation for the system of equations f x 0 with f in j with this cdc formulation the cell exclusion algorithm developed in 1 is generalized it is shown that the algorithm generalized can not only be applied assuredly to locate all the zeros of any functions f in j but it can do so much more efficiently and conveniently than the original algorithms as well

evolution strategies with exclusion based selection operators and a fourier series auxiliary function abstract to improve the efficiencies of evolutionary algorithms eas we have proposed a highly efficient speed up strategy in our previous research work the exclusion based selection operators these operators could efficiently prevent the individuals of eas from getting into the attractions of local optima through the search space shrinking method however when a global optimum of a minimization problem is located in a very narrow attraction the exclusion based selection operators may not be able to find this narrow attraction and delete this global optimum mistakenly making the algorithm unreliable in this paper we propose a new complementary efficient speed up strategy the fourier series auxiliary function this strategy could guide an algorithm to search for optima with narrow attractions efficiently and effectively and compensate the deficiency of the exclusion based selection operators on the algorithm s reliability we combine these two strategies together to search the global optima in parallel one for optima in normal attractions and the other for optima in very narrow attractions respectively incorporation of these two strategies with any known evolutionary algorithm leads to an accelerated version of the algorithm as a case study the new strategies have been incorporated into evolution strategies es yielding an accelerated exclusion and fourier series auxiliary function es the efes the efes is experimentally tested with a test suite containing 10 complex multimodal function optimization problems and compared against the standard es ses and the fast es fes the experiments all demonstrate that the efes consistently and significantly outperforms other two es in efficiency and solution quality

jointly constrained biconvex programming this paper presents a branch and bound algorithm for minimizing the sum of a convex function in x a convex function in y and a bilinear term in x and y over a closed set such an objective function is called biconvex with biconcave functions similarly defined the feasible region of this model permits joint constraints in x and y to be expressed the bilinear programming problem becomes a special case of the problem addressed in this paper we prove that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point the algorithm is proven to converge to a global solution of the nonconvex program we discuss extensions of the general model and computational experience in solving jointly constrained bilinear programs for which the algorithm has been implemented

lp narrowing a new strategy for finding all solutions of nonlinear equations an efficient algorithm is proposed for finding all solutions of systems of n nonlinear equations this algorithm is based on interval analysis and a new strategy called lp narrowing in the lp narrowing strategy boxes n dimensional rectangles in the solution domain containing no solution are excluded and boxes containing solutions are narrowed so that no solution is lost by using linear programming techniques since the lp narrowing is very powerful all solutions can be found very efficiently by numerical examples it is shown that the proposed algorithm could find all solutions of systems of 5000 50 000 nonlinear equations in practical computation time

an augmented singular transform and its partial newton method for finding new solutions to find new solutions through the information provided by previously found solution s this paper is first to develop a new singular transform to change the local basin barrier structure of the original problem in an infinite dimensional space and then to propose an augmented partial newton method to solve the transformed problem on the solution set mathematical justifications of the new formulation and method are established details on algorithm implementation are presented examples for two very different variational pde problems are carried out to illustrate the method their numerical results are displayed by profile contour plots and error convergence data the formulation and method developed in this paper can also be applied to solve multiple fixed point problems

construction of k lipschitz triangular norms and conorms from empirical data this paper examines the practical construction of k lipschitz triangular norms and conorms from empirical data we apply a characterization of such functions based on k convex additive generators and translate k convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients this is the basis of a simple linear spline fitting algorithm which guarantees k lipschitz property of the resulting triangular norms and conorms

a cell exclusion algorithm for determining all the solutions of a nonlinear system of equations abstract a new group of methods named cell exclusion algorithms ceas is developed for finding all the solutions of a nonlinear system of equations these types of algorithms different in principle from those of homotopy interval and cell mapping dynamical analysis approaches are based on cellular discretization and the use of a certain simple necessity test of the solutions the main advantages of the algorithms are their simplicity reliability and general applicability having all features of interval techniques but without using interval arithmetic and with complexity o log 1 e the algorithms improve significantly on both the interval algorithms and the cell mapping techniques theoretical analysis and numerical simulations both demonstrate that ceas are very efficient

weighted residual method for obtaining positive solutions of two point nonlinear boundary value problems this paper applies the weighted residual method to solving two point nonlinear boundary value problems that have at least one positive solution numerical verification is given revealing the efficiency and convenience of the method proposed comparison with the work of others is also illustrated

efficient and safe global constraints for handling numerical constraint systems numerical constraint systems are often handled by branch and prune algorithms that combine splitting techniques local consistencies and interval methods this paper first recalls the principles of tt quad a global constraint that works on a tight and safe linear relaxation of quadratic subsystems of constraints then it introduces a generalization of tt quad to polynomial constraint systems it also introduces a method to get safe linear relaxations and shows how to compute safe bounds of the variables of the linear constraint system different linearization techniques are investigated to limit the number of generated constraints tt quadsolver a new branch and prune algorithm that combines tt quad local consistencies and interval methods is introduced tt quadsolver has been evaluated on a variety of benchmarks from kinematics mechanics and robotics on these benchmarks it outperforms classical interval methods as well as constraint satisfaction problem solvers and it compares well with state of the art optimization solvers

an efficient procedure for solving a fuzzy relational equation with max archimedean t norm composition in the literature a necessary condition for minimal solutions of a fuzzy relational equation with max product composition shows that each of its components is either zero or the corresponding component s value of the greatest solution in this paper we first extend this necessary condition to the situation with max archimedean triangular norm t norm composition based on this necessary condition we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently furthermore rather than work with the actual equations we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions numerical examples with specific cases of the max archimedean t norm composition are provided to illustrate the procedure

isolated point of spectrum of p quasihyponormal operators let t b h be a bounded linear operator on a complex hilbert space h let 0 be an isolated point of t and let e 12 i 0 r t 1d be the riesz idempotent for 0 in this paper we prove that if t is a p quasihyponormal operator with 0 p 1 and 0 0 then e is self adjoint and eh ker t 0 ker t 0

smoothly generated archimedean approximation of continuous triangular norms a constructive method is given for approximating a given continuous triangular norm by a sequence of smoothly generated archimedean triangular norms in the uniform metric

subscalarity of p k quasihyponormal operators abstract in this paper we show that every p k quasihyponormal operator has a scalar extension and give some spectral properties of the scalar extensions of p k quasihyponormal operators as a corollary we get that such an operator with rich spectrum has a nontrivial invariant subspace finally we prove that the sum of a p hyponormal operator and an algebraic operator which are commuting is subscalar

on the use of aggregation operations in information fusion processes this position paper discusses the role of the existing body of fuzzy set aggregation operations in various kinds of problems where the process of fusion of items coming from several sources is central several kinds of membership functions can be useful according to the nature of the information to be merged numerical vs ordinal inputs preferences vs uncertain data observations vs constraints in each case some aggregation operations look more plausible or feasible than others the aim of this discussion is to suggest directions for putting at work the results of recent mathematical investigations in the structure of aggregation operations

on archimedean triangular norms abstract the behaviour of the additive generator functions related to a sequence of convergent continuous archimedean triangular norm where the limit triangular norm is continuous archimedean is examined in this paper it is proved that the related generator functions converge to the generator function of the limit triangular norm in some sense under the assumption that the limit triangular norm is strict a bit weaker convergence is proved if the limit triangular norm has 0 divisor an example is given for the fact that the stronger type of convergence cannot be obtained in the 0 divisor limit case

global optimization of mixed integer nonlinear programs a theoretical and computational study this work addresses the development of an efficient solution strategy for obtaining global optima of continuous integer and mixed integer nonlinear programs towards this end we develop novel relaxation schemes range reduction tests and branching strategies which we incorporate into the prototypical branch and bound algorithm in the theoretical algorithmic part of the paper we begin by developing novel strategies for constructing linear relaxations of mixed integer nonlinear programs and prove that these relaxations enjoy quadratic convergence properties we then use lagrangian linear programming duality to develop a unifying theory of domain reduction strategies as a consequence of which we derive many range reduction strategies currently used in nonlinear programming and integer linear programming this theory leads to new range reduction schemes including a learning heuristic that improves initial branching decisions by relaying data across siblings in a branch and bound tree finally we incorporate these relaxation and reduction strategies in a branch and bound algorithm that incorporates branching strategies that guarantee finiteness for certain classes of continuous global optimization problems in the computational part of the paper we describe our implementation discussing wherever appropriate the use of suitable data structures and associated algorithms we present computational experience with benchmark separable concave quadratic programs fractional 0 1 programs and mixed integer nonlinear programs from applications in synthesis of chemical processes engineering design just in time manufacturing and molecular design

a new exclusion test for finding the global minimum exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain these algorithms are based on a minimization condition that can be applied to each cell in the domain in this paper we consider lipschitz functions of order a and give a new minimization condition for the exclusion algorithm furthermore convergence and complexity results are presented for such algorithm

generators of copulas and aggregation the most applied class of copulas for fitting purposes is undoubtedly the class of archimedean copulas due to their representation by means of single functions of one variable i e by means of additive generators or the corresponding pseudo inverses in this paper we characterize aggregation functions preserving additive generators pseudo inverses of additive generators of archimedean copulas as a by product we obtain an efficient method to construct new additive generators from some given ones

efficiency speed up strategies for evolutionary computation fundamentals and fast gas through identifying the main causes of low efficiency of the currently known evolutionary algorithms a set of six efficiency speed up strategies are suggested analyzed and partially explored including those of the splicing decomposable representation scheme the exclusion based selection operators the few generation ended ec search the low resolution computation with reinitialization and the coevolution like decomposition incorporation of the strategies with any known evolutionary algorithm leads to an accelerated version of the algorithm on the basis of problem space discretization the proposed strategies accelerate evolutionary computation via a best so far solution guided exclusion based space shrinking scheme with this scheme an arbitrarily high precision resolution solution of a high dimensional problem can be obtained by means of a successive low resolution search in low dimensional search spaces as a case study the developed strategies have been endowed with genetic algorithms gas yielding an accelerated genetic evolutionary algorithm the fast gas the fast gas are experimentally tested with a test suit containing 10 complex multimodal function optimization problems and a difficult real life problem the moment matching problem for inverse to the fractal encoding of the spleenwort fern the performance of the fast ga is compared against the standard ga sga and the forking ga fga that is one of the most recent and fairly established variants of gas the experiments all demonstrate that the fast gas consistently and significantly outperform the sga and fga in efficiency and solution quality in the test cases besides the speed up of efficiency other visible features of the fast gas include i no premature convergence occurs ii better convergence capability to global optimum and iii variable high precision solutions attainable all these support the validity and usefulness of the developed strategies

accelerating filtering techniques for numeric csps search algorithms for solving numeric csps constraint satisfaction problems make an extensive use of filtering techniques in this paper we show how those filtering techniques can be accelerated by discovering and exploiting some regularities during the filtering process two kinds of regularities are discussed cyclic phenomena in the propagation queue and numeric regularities of the domains of the variables we also present in this paper an attempt to unify numeric csps solving methods from two distinct communities that of csp in artificial intelligence and that of interval analysis

finding all solutions of separable systems of piecewise linear equations using integer programming abstract finding all solutions of nonlinear or piecewise linear equations is an important problem which is widely encountered in science and engineering various algorithms have been proposed for this problem however the implementation of these algorithms are generally difficult for non experts or beginners in this paper an efficient method is proposed for finding all solutions of separable systems of piecewise linear equations using integer programming in this method we formulate the problem of finding all solutions by a mixed integer programming problem and solve it by a high performance integer programming software such as glpk scip or cplex it is shown that the proposed method can be easily implemented without making complicated programs it is also confirmed by numerical examples that the proposed method can find all solutions of medium scale systems of piecewise linear equations in practical computation time

riesz projections for a class of hilbert space operators abstract a hilbert space operator t t b h is totally hereditarily normaloid t thn if every part and also every invertible part of t is normaloid the class thn is large it is proved that if a t thn is such that the isolated eigenvalues of t are normal then the riesz projection p associated with a iso t is self adjoint and p h t 1 0 t 1 0

errata computing all solutions to polynomial systems using homotopy continuation in a previous paper we described a new method for defining homotopies for finding all solutions to polynomial systems a major feature of this new approach is that the start system for the homotopy need not be a random or generic system also homotopy paths are strictly increasing in the homotopy parameter in this paper we establish some principles of implementation and report on the performance of programs that use the new homotopies a feature of our implementation is that we eliminate divergent paths entirely we include performance statistics for homotopies derived from more traditional approaches for comparison generally the new approach is faster and more reliable