lagrangean surrogate relaxation for generalized assignment problems abstract this work presents lagrangean surrogate relaxation to the problem of maximum profit assignment of n tasks to m agents n m such that each task is assigned to only one agent subject to capacity constraints on the agents the lagrangean surrogate relaxation combines usual lagrangean and surrogate relaxations relaxing first a set of constraints in the surrogate way then the lagrangean relaxation of the surrogate constraint is obtained and approximately optimized one dimensional dual the lagrangean surrogate is compared with the usual lagrangean relaxation on a computational study using a large set of instances the dual bounds are the same for both relaxations but the lagrangean surrogate can give improved local bounds at the application of a subgradient method resulting in less computational times three relaxations are derived for the problem the first relaxation considers a vector of multipliers for the capacity constraints the second for the assignment constraints and the other for the lagrangean decomposition constraints relaxation multipliers are used with efficient constructive heuristics to find good feasible solutions the application of a lagrangean surrogate approach seems very promising for large scale problems

a new exchange method for convex semi infinite programming in this paper we propose a new exchange method for solving convex semi infinite programming csip problems we introduce a new dropping rule in the proposed exchange algorithm which only keeps those active constraints with positive lagrange multipliers moreover we exploit the idea of looking for eta infeasible indices of the lower level problem as the adding rule in our algorithm hence the algorithm does not require to solve a maximization problem over the index set at each iteration it only needs to find some points such that a certain computationally easy criterion is satisfied under some reasonable conditions the new adding dropping rule guarantees that our algorithm provides an approximate optimal solution for the csip problem in a finite number of iterations in the numerical experiments we apply the proposed algorithm to solve some test problems from the literature including some medium sized problems from complex approximation theory and fir filter design we compare our algorithm with an existing central cutting plane algorithm and with the semi infinite solver fseminf in matlab toolbox and we find that our algorithm solves the csip problem much faster for the fir filter design problem we show that our algorithm solves the problem better than some algorithms that were technically established for the problem

on initial instantaneous jumps of singular systems this paper is concerned with instantaneous jumps in the state trajectory of a singular system it is shown that such jumps generically exist at the initial time due to inconsistent initial states the formula for the jumps is derived which indicates that the jumps linearly depend on the initial state moreover the set of all initial states which do not cause any state jumps for any output feedback is characterized and is revealed to be a linear subspace in the meantime the necessary and sufficient conditions are given for the existence of an output feedback to suppress completely the jumps for a given initial state finally we formulate the problem of designing an output feedback not only to stabilize the plant but also to achieve minimum initial jumps as a minimization problem

the equilibrium generalized assignment problem and genetic algorithm abstract the well known generalized assignment problem gap is to minimize the costs of assigning n jobs to m capacity constrained agents or machines such that each job is assigned to exactly one agent this problem is known to be np hard and it is hard from a computational point of view as well in this paper follows from practical point of view in real systems the gap is extended to the equilibrium generalized assignment problem egap and the equilibrium constrained generalized assignment problem ecgap a heuristic equilibrium strategy based genetic algorithm ga is designed for solving the proposed egap finally to verify the computational efficiency of the designed ga some numerical experiments are performed on some known benchmarks the test results show that the designed ga is very valid for solving egap

lagrangian relaxation guided problem space search heuristics for generalized assignment problems we develop and test a heuristic based on lagrangian relaxation and problem space search to solve the generalized assignment problem gap the heuristic combines the iterative search capability of subgradient optimization used to solve the lagrangian relaxation of the gap formulation and the perturbation scheme of problem space search to obtain high quality solutions to the gap we test the heuristic using different upper bound generation routines developed within the overall mechanism using the existing problem data sets of various levels of difficulty and sizes including the challenging largest instances we observe that the heuristic with a specific version of the upper bound routine works well on most of the benchmark instances known and provides high quality solutions quickly an advantage of the approach is its generic nature simplicity and implementation flexibility

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

a nonsmooth levenberg marquardt method for solving semi infinite programming problems in this paper we first transform the semi infinite programming problem into the kkt system by the techniques in d h li l qi j tam s y wu a smoothing newton method for semi infinite programming j global optim 30 2004 169 194 l qi s y wu g l zhou semismooth newton methods for solving semi infinite programming problems j global optim 27 2003 215 232 then a nonsmooth and inexact levenberg marquardt method is proposed for solving this kkt system based on h dan n yamashita m fukushima convergence properties of the inexact levenberg marquardt method under local error bound conditions optimim methods softw 11 2002 605 626 this method is globally and superlinearly even quadratically convergent finally some numerical results are given

nonlinearly constrained discrete time optimal control problems we consider a class of constrained discrete time optimal control problems we use the discrete version of the control parametrization concept together with a simple constraint transcription to devise a computational algorithm for solving this class of problems convergence analysis is given to support this numerical approach for illustration three nontrivial optimal control problems are solved using it

an exact penalty function approach to all time step constrained discrete time optimal control problems a new solution method for a general class of discrete time optimal control problems with all time step constraints is proposed it uses a constraint transcription to incorporate the all time step constraints into the cost functional we show that the weighting factor of the penalty term does not need to approach infinity for convergence this is in contrast to the conventional penalty function approach for solving constrained optimization problems

a new computational algorithm for functional inequality constrained optimization problems abstract in this note a computational algorithm is devised for solving a class of functional inequality constrained optimization problems based on a penalty function for illustration a numerical example is solved

nonlinear robust optimization via sequential convex bilevel programming in this paper we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min max problems which arise in the context of semi infinite programming here our main motivation are nonlinear inequality constrained robust optimization problems in the first part of the paper we propose a conservative approximation strategy for such nonlinear and non convex robust optimization problems under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given we show how to formulate a lower level concave min max problem which approximates the robust counterpart in a conservative way this approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties in the second part of the paper we review existing theory on optimality conditions for nonlinear lower level concave min max problems which arise in the context of semi infinite programming regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem we end up with a structured mathematical program with complementarity constraints mpcc the special hierarchical structure of this mpcc can be exploited in a novel sequential convex bilevel programming algorithm we discuss the surprisingly strong global and locally quadratic convergence properties of this method which can in this form neither be obtained with existing sqp methods nor with interior point relaxation techniques for general mpccs finally we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example

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

moments of the ratio of quadratic forms in non normal variables with econometric examples abstract in this paper we have provided a general result on the higher order approximate moments of the ratio of quadratic forms in the non normal vector the results for the normal case are then presented as a special case of this result it is also indicated that the results for a large class of econometric estimators and test statistics can be obtained by using our general result

discretization in semi infinite programming the rate of convergence the discretization approach for solving semi infinite optimization problems is considered we are interested in the convergence rate of the error between the solution of the semi infinite problem and the solution of the discretized program depending on the discretization mesh size it will be shown how this rate depends on whether the minimizer is strict of order one or two and on whether the discretization includes boundary points of the index set in a specific way this is done for ordinary and for generalized semi infinite problems

a semi infinite programming algorithm for solving optimal power flow with transient stability constraints this paper proposes a new algorithm for solving a type of complicated optimal power flow opf problems in power systems i e opf problems with transient stability constraints ots the ots is converted into a semi infinite programming sip via some suitable function analysis then based on the kkt system of the reformulated sip a smoothing quasi newton algorithm is presented in which the numerical integration is used the convergence of the algorithm is established an ots problem in power system is tested which shows that the proposed algorithm is promising

a lagrangian dual based branch and bound algorithm for the generalized multi assignment problem this paper develops a lagrangian dual based branch and bound algorithm for the generalized multi assignment problem gmap which includes the well known generalized assignment problem gap as a special case in gmap an object may be required to be duplicated in multiple locations we develop a lagrangian dual ascent algorithm for gmap this dual ascent and the subgradient search each possess advantages that can be combined to develop a new lagrangian dual search algorithm the latter algorithm when incorporated into a branch and bound algorithm as the lower bounding scheme can accelerate the search process computational results demonstrate the efficiency and robustness of this branch and bound algorithm not only for gmaps but for gaps that are more difficult than could be solved by previous algorithms

local optimization of dynamic programs with guaranteed satisfaction of path constraints an algorithm is proposed for locating a feasible point satisfying the kkt conditions to a specified tolerance of feasible inequality path constrained dynamic programs pcdp within a finite number of iterations the algorithm is based on iteratively approximating the pcdp by restricting the right hand side of the path constraints and enforcing the path constraints at finitely many time points the main contribution of this article is an adaptation of the semi infinite program sip algorithm proposed in mitsos 2011 to pcdp it is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first order kkt conditions of the pcdp to a specified tolerance the main assumptions are i availability of a nonlinear program nlp local solver that generates a kkt point of the constructed approximation to pcdp at each iteration if this problem is indeed feasible ii existence of a slater point of the pcdp that also satisfies the first order kkt conditions of the pcdp to a specified tolerance iii all kkt multipliers are nonnegative and uniformly bounded with respect to all iterations the performance of the algorithm is analyzed through two numerical case studies

a new proof of the strong duality theorem for semidefinite programming semidefinite programs are convex optimization problems arising in a wide variety of applications and are the extension of linear programming most methods for linear programming have been generalized to semidefinite programs just as in linear programming duality theorem plays a basic and an important role in theory as well as in algorithmics based on the discretization method and convergence property this paper proposes a new proof of the strong duality theorem for semidefinite programming which is different from other common proofs and is more simple

brief paper optimal control problems with a continuous inequality constraint on the state and the control we consider an optimal control problem with a nonlinear continuous inequality constraint both the state and the control are allowed to appear explicitly in this constraint by discretizing the control space and applying a novel transformation a corresponding class of semi infinite programming problems is derived a solution of each problem in this class furnishes a suboptimal control for the original problem furthermore we show that such a solution can be computed efficiently using a penalty function method on the basis of these two ideas an algorithm that computes a sequence of suboptimal controls for the original problem is proposed our main result shows that the cost of these suboptimal controls converges to the minimum cost for illustration an example problem is solved

the second order bias and mean squared error of nonlinear estimators abstract despite the now widespread use of nonlinear estimators their finite sample properties have received very little attention in either the statistics or econometrics literature we partially redress this problem by deriving and examining the second order bias and mean squared error of a fairly wide class of nonlinear estimators which includes nonlinear least squares maximum likelihood and many generalized method of moments estimators as special cases a number of examples are provided the results from a monte carlo exercise demonstrate how the results can be applied for improved inferences

the second order bias and mean squared error of estimators in time series models we develop analytical results on the second order bias and mean squared error of estimators in time series models these results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time series models and they are valid for both normal and nonnormal samples of observations and where the regressors are stochastic the estimators included are the generalized method of moments maximum likelihood least squares and other extremum estimators our general results are applied to four time series models we investigate the effects of nonnormality on the second order bias results for two of these models while for all four models the second order bias and mean squared error results are given under normality numerical results for some of these models are also presented

uncertain convex programs randomized solutions and confidence levels many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or instance parameter two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty robust optimization and chance constrained optimization robust optimization is a deterministic paradigm where one seeks a solution which simultaneously satisfies all possible constraint instances in chance constrained optimization a probability distribution is instead assumed on the uncertain parameters and the constraints are enforced up to a pre specified level of probability unfortunately however both approaches lead to computationally intractable problem formulations

lipschitz modulus of linear and convex inequality systems with the hausdorff metric this paper analyzes the lipschitz behavior of the feasible set mapping associated with linear and convex inequality systems in mathbb r n to start with we deal with the parameter space of linear finite semi infinite systems identified with the corresponding sets of coefficient vectors which are assumed to be closed subsets of mathbb r n 1 in this framework the size of perturbations is measured by means of the extended hausdorff distance a direct antecedent extensively studied in the literature comes from considering the parameter space of all linear systems with a fixed index set t where the chebyshev extended distance is used to measure perturbations in the present work we propose an appropriate indexation strategy which allows us to establish the equality of the lipschitz moduli of the feasible set mappings in both parametric contexts as well as to benefit from existing results in the chebyshev setting for transferring them to the hausdorff one in a second stage the possibility of perturbing directly the set of coefficient vectors of a linear system leads to new contributions on the lipschitz behavior of convex systems via linearization techniques

a path relinking approach with ejection chains for the generalized assignment problem the generalized assignment problem is a classical combinatorial optimization problem known to be np hard it can model a variety of real world applications in location allocation machine assignment and supply chains the problem has been studied since the late 1960s and computer codes for practical applications emerged in the early 1970s we propose a new algorithm for this problem that proves to be more effective than previously existing methods the algorithm features a path relinking approach which is a mechanism for generating new solutions by combining two or more reference solutions it also features an ejection chain approach which is embedded in a neighborhood construction to create more complex and powerful moves computational comparisons on benchmark instances show that the method is not only effective in general but is especially effective for types d and e instances which are known to be very difficult

impulse response matching estimators for dsge models abstract the existing asymptotic theory for var based impulse response matching estimators of the structural parameters of dsge models does not cover situations in which the number of impulse responses exceeds the number of var model parameters we establish the consistency of the estimator in this situation we derive its asymptotic distribution and we show how this distribution can be approximated by bootstrap methods we also demonstrate that under our assumptions special care is needed to ensure the asymptotic validity of bayesian methods of inference finally we show how to deal with weak identification both under our assumptions and under standard assumptions

a general method for third order bias and variance corrections on a nonlinear estimator motivated by a recent study of bao and ullah 2007a on finite sample properties of mle in the pure sar spatial autoregressive model a general method for third order bias and variance corrections on a nonlinear estimator is proposed based on stochastic expansion and bootstrap working with concentrated estimating equation simplifies greatly the high order expansions for bias and variance a simple bootstrap procedure overcomes a major difficulty in analytically evaluating expectations of various quantities in the expansions the method is then studied in detail using a more general sar model with its effectiveness in correcting bias and improving inference fully demonstrated by extensive monte carlo experiments compared with the analytical approach the proposed approach is much simpler and has a much wider applicability the validity of the bootstrap procedure is formally established the proposed method is then extended to the case of more than one nonlinear estimator

bias correction in generalized linear models summary in this paper we derive general formulae for first order biases of maximum likelihood estimates of the linear parameters linear predictors the dispersion parameter and fitted values in generalized linear models these formulae may be implemented in the glim program to compute bias corrected maximum likelihood estimates to order n 1 where n is the sample size with minimal effort by means of a supplementary weighted regression for linear logistic models it is shown that the asymptotic bias vector of j8 is almost collinear with f3 the approximate formula flp m for the bias of s in logistic models where p dim and m e mi is the sum of the binomial indices is derived and checked numerically

bias assessment and reduction in linear error correction models abstract the small sample bias of the ordinary least squares coefficient estimator for dynamic regression models with innovation errors and lagged dependent and strongly exogenous explanatory variables is approximated through both small disturbance and large sample asymptotics results for the standard armax p 0 k model are obtained and also for such models under linear parameter constraints and variable transformations these approximations are then used to construct corrected estimators for the parameters of interest in higher order dynamic models including the empirically highly relevant linear error correction model by simulating two empirical cases the corrected estimators obtained via large sample asymptotics are shown to have more attractive location and efficiency properties than ordinary least squares

discretization method for semi definite programming semi definite programs are convex optimization problems arising in a wide variety of applications and the extension of linear programming most methods for linear programming have been generalized to semi definite programs this paper discusses the discretization method in semi definite programming the convergence and the convergent rate of error between the optimal value of the semi definite programming problems and the optimal value of the discretized problems are obtained an approximately optimal division is given under certain assumptions with the significance of the convergence property the duality result in semi definite programs is proved in a simple way which is different from the other common proofs

tabu search for the multilevel generalized assignment problem abstract the multilevel generalized assignment problem mgap differs from the classical gap in that agents can perform tasks at more than one efficiency level important manufacturing problems such as lot sizing can be formulated as mgaps however the large number of variables in the related 0 1 integer program makes the use of commercial optimization packages impractical in this paper we present a heuristic approach to the solution of the mgap which consists of a novel application of tabu search ts our ts method employs neighborhoods defined by ejection chains that produce moves of greater power without significantly increasing the computational effort

a hybrid heuristic for the generalized assignment problem abstract the objective of this study is to develop a hybrid heuristic hh for solving the generalized assignment problem gap and conduct a computational comparison with the leading alternative heuristic approaches hh is designed around the two best known heuristics heuristic gap hgap and variable depth search heuristic vdsh previous performance characteristic studies have shown that hgap dominates vdsh in terms of solution cpu time while vdsh obtains solutions of 13 to 300 better quality within a reasonable time the main idea in this paper is to hybridize the two approaches such that the inherent values of both heuristics are realized

asymptotic expansions of the information matrix test statistic the information matrix im test is shown to have a finite sample distribution which is poorly approximated by its asymptotic x 2 distribution in models and sample sizes commonly encountered in applied econometric research the quality of the x2 approximation depends upon the method chosen to compute the test failure to exploit restrictions on the covariance matrix of the test can lead to a test with appalling finite sample properties order o n 1 approximations to the exact distribution of an efficient form of the im test are reported these are developed from asymptotic expansions of the edgeworth and cornish fisher types they are compared with monte carlo estimates of the finite sample distribution of the test and are found to be superior to the usual x2 approximations in sample sizes of the magnitude found in applied micro econometric work the methods developed in the paper are applied to normal and exponential models and to normal regression models results are provided for the full im test and for heteroskedasticity and nonnormality diagnostic tests which are special cases of the im test in geieral the quality of alternative approximations is sensitive to covariate design however commonly used nonnormality tests are found to have distributions which to order o n 1 are invariant under changes in covariate design this leads to simple design and parameter invariant size corrections for nonnormality tests

improved lagrangean decomposition an application to the generalized assignment problem abstract recently two new ways of obtaining improved lagrangean bounds have been suggested lagrangean decomposition and bound improving sequences in this work we will obtain a lagrangean approach combining the two ideas mentioned above theoretical results are provided about the sharpness of the bounds obtained by the combined approach for the general case as well as an application to the generalized assignment problem computational experience is reported

a new computational method for the functional inequality constrained minimax optimization problem in this paper we consider a general class of functional inequality constrained minimax optimization problems this problem is first converted into a semi infinite programming problem then an auxiliary cost function is constructed based on a positive saturated function the smallest zero of this auxiliary cost function is equal to the minimal cost of the semi infinite programming problem however this auxiliary cost function is nonsmooth thus a smoothing function is introduced then an efficient computational procedure is developed to estimate the smallest zero of this auxiliary cost function furthermore an error bound is obtained to validate the accuracy of the approximate solution for illustration two numerical examples are solved using the proposed approach

convergence analysis of some algorithms for solving nonsmooth equations this paper presents convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally lipschitzian functions for the directional derivative based and the generalized jacobian based newton methods both the iterates and the corresponding function values are locally superlinearly convergent globally a limiting point of the iterate sequence generated by the damped directional derivative based newton method is a zero of the system if and only if the iterate sequence converges to this point and the stepsize eventually becomes one provided that the system is strongly bd regular and semismooth at this point in this case the convergence is superlinear a general attraction theorem is presented which can be applied to two algorithms proposed by han pang and rangaraj a hybrid method which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent is also presented

sensitivity analysis and identification of kinetic parameters in batch fermentation of glycerol a nonlinear dynamical system was established in our preceding work to describe the batch and continuous bioconversions of glycerol to 1 3 propanediol by klebsiella pneumoniae the purpose of this article is to analyze the sensitivity of kinetic parameters of the dynamical system and identify their values from experiment a global sensitivity analysis approach is constructed by combining the local technique with the monte carlo method with only those parameters of higher sensitivity as design variables we propose a parameter identification model and solve it by a gradient based simulated annealing algorithm numerical results show that our methods are feasible and efficient

an interior point sequential quadratic programming type method for log determinant semi infinite programs abstract in this paper we consider a nonlinear semi infinite program that minimizes a function including a log determinant logdet function over positive definite matrix constraints and infinitely many convex inequality constraints we call this problem siplog where sip stands for semi infinite program and log comes from log det function the main purpose of the paper is to develop an algorithm for efficiently computing a karush kuhn tucker kkt point for the siplog more specifically we propose an interior point sequential quadratic programming type method that solves inexactly a sequence of semi infinite quadratic programs approximating the siplog furthermore to generate a search direction in the dual matrix space associated with the semi definite constraint we solve scaled newton equations that yield the family of monteiro zhang directions we prove that the proposed method weakly converges to a kkt point under some mild assumptions finally we conduct some numerical experiments to demonstrate the efficiency of the proposed method

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

nondifferentiable optimization algorithm for designing control systems having singular value inequalities it has been known for some time that many control system design requirements can be expressed as differentiable inequalities more recently it has been shown that important structural properties such as robustness and low noise sensitivity can be expressed as nondifferentiable inequalities involving the singular values of a system or return difference transfer function matrix this paper presents an optimization algorithm which permits all these constraints to be considered

on the mathematical foundations of nondifferentiable optimization in engineering design it is shown by example that a large class of engineering design problems can be transcribed into the form of a canonical optimization problem with inequality constraints involving mar functions such problems are commonly referred to as semi infinite optimization problems the bulk of this paper is devoted to the development of a mathematical theory for the construction of first order nondifferentiable optimization algorithms related to phase i phase ii methods of feasible directions which solve these semi infinite optimization problems the applicability of the theory is illustrated with examples that are relevant to engineering design

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

a simple computational procedure for optimization problems with functional inequality constraints in this note a simple computational procedure is given for solving a class of optimization problems where an objective function is to be minimized subject to conventional inequality constraints as well as to inequality constraints of the functional type

effective algorithm and heuristic for the generalized assignment problem we present new branch and bound algorithm for the generalized assignment problem a standard subgradient method sm used at each node of the decision tree to solve the lagrangian dual provides an upper bound our key contribution in this paper is a new heuristic applied at each iteration of the sm which tries to exploit the solution of the relaxed problem by solving a smaller generalized assignment problem the feasible solution found is then subjected to a solution improvement heuristic we consider processing the root node as a lagrangian heuristic computational comparisons are made with new existing methods

solving semi infinite optimization problems with interior point techniques we introduce a new numerical solution method for semi infinite optimization problems with convex lower level problems the method is based on a reformulation of the semi infinite problem as a stackelberg game and the use of regularized nonlinear complementarity problem functions this approach leads to central path conditions for the lower level problems where for a given path parameter a smooth nonlinear finite optimization problem has to be solved the solution of the semi infinite optimization problem then amounts to driving the path parameter to zero we show convergence properties of the method and give a number of numerical examples from design centering and from robust optimization where actually so called generalized semi infinite optimization problems are solved the presented method is easy to implement and in our examples it works well for dimensions of the semi infinite index set at least up to 150

a standard branch and bound approach for nonlinear semi infinite problems this paper considers nonlinear semi infinite problems which contain at least one semi infinite constraint sic the standard branch and bound algorithm is adapted to such problems by extending usual upper and lower bounding techniques for nonlinear inequality constraints to sics this is achieved by defining the interval evaluation of parametrized functions and their generalized gradients by also adapting numerical constraint programming techniques to quantified inequalities and by introducing linear relaxations and restrictions for sics the overall efficiency of our algorithm is demonstrated on a standard set of benchmarks from the literature in comparison with the best state of the art alternative

bees algorithm for generalized assignment problem bees algorithm ba is a new member of meta heuristics ba tries to model natural behavior of honey bees in food foraging honey bees use several mechanisms like waggle dance to optimally locate food sources and to search new ones this makes them a good candidate for developing new algorithms for solving optimization problems in this paper a brief review of ba is first given afterwards development of a ba for solving generalized assignment problems gap with an ejection chain neighborhood mechanism is presented gap is a np hard problem many meta heuristic algorithms were proposed for its solution so far ba is generally applied to continuous optimization in order to investigate the performance of ba on a complex integer optimization problem an attempt is made in this paper an extensive computational study is carried out and the results are compared with several algorithms from the literature

an approximation algorithm for the generalized assignment problem the generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs each job is to be processed by exactly one machine processing jobj on machinei requires timep ij and incurs a cost ofc ij each machinei is available fort i time units and the objective is to minimize the total cost incurred our main result is as follows there is a polynomial time algorithm that given a valuec either proves that no feasible schedule of costc exists or else finds a schedule of cost at mostc where each machinei is used for at most 2t i time units we also extend this result to a variant of the problem where instead of a fixed processing timep ij there is a range of possible processing times for each machine job pair and the cost linearly increases as the processing time decreases we show that these results imply a polynomial time 2 approximation algorithm to minimize a weighted sum of the cost and the makespan i e the maximum job completion time we also consider the objective of minimizing the mean job completion time we show that there is a polynomial time algorithm that given valuesm andt either proves that no schedule of mean job completion timem and makespant exists or else finds a schedule of mean job completion time at mostm and makespan at most 2t

generalized semi infinite programming a tutorial this tutorial presents an introduction to generalized semi infinite programming gsip which in recent years became a vivid field of active research in mathematical programming a gsip problem is characterized by an infinite number of inequality constraints and the corresponding index set depends additionally on the decision variables there exist a wide range of applications which give rise to gsip models some of them are discussed in the present paper furthermore geometric and topological properties of the feasible set and in particular the difference to the standard semi infinite case are analyzed by using first order approximations of the feasible set corresponding constraint qualifications are developed then necessary and sufficient first and second order optimality conditions are presented where directional differentiability properties of the optimal value function of the so called lower level problem are used finally an overview of numerical methods is given

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

a truncated projected newton type algorithm for large scale semi infinite programming in this paper a truncated projected newton type algorithm is presented for solving large scale semi infinite programming problems this is a hybrid method of a truncated projected newton direction and a modified projected gradient direction the truncated projected newton method is used to solve the constrained nonlinear system in order to guarantee global convergence a robust loss function is chosen as the merit function and the projected gradient method inserted is used to decrease the merit function this algorithm is suitable for handling large scale problems and possesses superlinear convergence rate the global convergence of this algorithm is proved and the convergence rate is analyzed the detailed implementation is discussed and some numerical tests for solving large scale semi infinite programming problems with examples up to 2000 decision variables are reported

bias in the estimation of the mean reversion parameter in continuous time models abstract it is well known that for continuous time models with a linear drift standard estimation methods yield biased estimators for the mean reversion parameter both in finite discrete samples and in large in fill samples in this paper we obtain two expressions to approximate the bias of the least squares maximum likelihood estimator of the mean reversion parameter in the ornstein uhlenbeck process with a known long run mean when discretely sampled data are available the first expression mimics the bias formula of marriott and pope 1954 for the discrete time model simulations show that this expression does not work satisfactorily when the speed of mean reversion is slow slow mean reversion corresponds to the near unit root situation and is empirically realistic for financial time series an improvement is made in the second expression where a nonlinear correction term is included into the bias formula it is shown that the nonlinear term is important in the near unit root situation simulations indicate that the second expression captures the magnitude the curvature and the non monotonicity of the actual bias better than the first expression

global optimum design of uniform fir filter bank with magnitude constraints the optimum design of a uniform finite impulse response filter bank can be formulated as a nonlinear semi infinite optimization problem however this optimization problem is nonconvex with infinitely many inequality constraints in this paper we propose a new hybrid approach for solving this highly challenging nonlinear nonconvex semi infinite optimization problem in this approach a gradient based method is used in conjunction with a filled function method to determine a global minimum of the problem this new hybrid approach finds an optimal result independent of the initial guess of the solution the method is applied to some existing examples the results obtained are superior to those obtained by other existing methods

relaxation based bounds for semi infinite programs finite formulations are presented for the calculation of lower and upper bounds on the optimal solution value of semi infinite programs sips involving smooth potentially nonconvex objective function and constraints the lower bounding problem is obtained by a formulation that combines the first and second order kkt necessary conditions of the lower level problem with a discretization of the parameter set the resulting mathematical program with equilibrium constraints mpec is a relaxation of the original sip and furnishes valid lower bounds if the parameter set is subdivided the optimal solution value of the lower bounding problem converges to the optimal solution value of the sip the upper bounding problem is based on convex and linear relaxations of the lower level problem resulting in a restriction of the sip if the parameter set is subdivided the constructed relaxations converge to the original lower level program the existence of sip slater points ensures convergence of the upper bounding problems to the optimal solution value of the sip several alternatives for the upper bounding problem are presented and discussed numerical results are presented for a number of test problems from the literature