Results 1  10
of
61
Engineering and economic applications of complementarity problems
 SIAM Review
, 1997
"... Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions f ..."
Abstract

Cited by 127 (24 self)
 Add to MetaCart
Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Successive Overrelaxation for Support Vector Machines
 IEEE Transactions on Neural Networks
, 1998
"... Successive overrelaxation (SOR) for symmetric linear complementarity problems and quadratic programs [11, 12, 9] is used to train a support vector machine (SVM) [20, 3] for discriminating between the elements of two massive datasets, each with millions of points. Because SOR handles one point at a t ..."
Abstract

Cited by 66 (14 self)
 Add to MetaCart
Successive overrelaxation (SOR) for symmetric linear complementarity problems and quadratic programs [11, 12, 9] is used to train a support vector machine (SVM) [20, 3] for discriminating between the elements of two massive datasets, each with millions of points. Because SOR handles one point at a time, similar to Platt's sequential minimal optimization (SMO) algorithm [18] which handles two constraints at a time, it can process very large datasets that need not reside in memory. The algorithm converges linearly to a solution. Encouraging numerical results are presented on datasets with up to 10 million points. Such massive discrimination problems cannot be processed by conventional linear or quadratic programming methods, and to our knowledge have not been solved by other methods. 1 Introduction Successive overrelaxation, originally developed for the solution of large systems of linear equations [16, 15] has been successfully applied to mathematical programming problems [4, 11, 12, 1...
Interfaces to PATH 3.0: Design, Implementation and Usage
 Computational Optimization and Applications
, 1998
"... Several new interfaces have recently been developed requiring PATH to solve a mixed complementarity problem. To overcome the necessity of maintaining a different version of PATH for each interface, the code was reorganized using objectoriented design techniques. At the same time, robustness issues ..."
Abstract

Cited by 48 (17 self)
 Add to MetaCart
Several new interfaces have recently been developed requiring PATH to solve a mixed complementarity problem. To overcome the necessity of maintaining a different version of PATH for each interface, the code was reorganized using objectoriented design techniques. At the same time, robustness issues were considered and enhancements made to the algorithm. In this paper, we document the external interfaces to the PATH code and describe some of the new utilities using PATH. We then discuss the enhancements made and compare the results obtained from PATH 2.9 to the new version. 1 Introduction The PATH solver [12] for mixed complementarity problems (MCPs) was introduced in 1995 and has since become the standard against which new MCP solvers are compared. However, the main user group for PATH continues to be economists using the MPSGE preprocessor [36]. While developing the new PATH implementation, we had two goals: to make the solver accessible to a broad audience and to improve the effecti...
A Penalized FischerBurmeister NcpFunction: Theoretical Investigation And Numerical Results
, 1997
"... We introduce a new NCPfunction that reformulates a nonlinear complementarity problem as a system of semismooth equations \Phi(x) = 0. The new NCPfunction possesses all the nice properties of the FischerBurmeister function for local convergence. In addition, its natural merit function \Psi(x) = ..."
Abstract

Cited by 43 (12 self)
 Add to MetaCart
We introduce a new NCPfunction that reformulates a nonlinear complementarity problem as a system of semismooth equations \Phi(x) = 0. The new NCPfunction possesses all the nice properties of the FischerBurmeister function for local convergence. In addition, its natural merit function \Psi(x) = 1 2 \Phi(x) T \Phi(x) has all the nice features of the KanzowYamashitaFukushima merit function for global convergence. In particular, the merit function has bounded level sets for a monotone complementarity problem with a strictly feasible point. This property allows the existing semismooth Newton methods to solve this important class of complementarity problems without additional assumptions. We investigate the properties of a semismooth Newtontype method based on the new NCPfunction and apply the method to a large class of complementarity problems. The numerical results indicate that the new algorithm is extremely promising.
Algorithms For Complementarity Problems And Generalized Equations
, 1995
"... Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult pr ..."
Abstract

Cited by 41 (5 self)
 Add to MetaCart
Recent improvements in the capabilities of complementarity solvers have led to an increased interest in using the complementarity problem framework to address practical problems arising in mathematical programming, economics, engineering, and the sciences. As a result, increasingly more difficult problems are being proposed that exceed the capabilities of even the best algorithms currently available. There is, therefore, an immediate need to improve the capabilities of complementarity solvers. This thesis addresses this need in two significant ways. First, the thesis proposes and develops a proximal perturbation strategy that enhances the robustness of Newtonbased complementarity solvers. This strategy enables algorithms to reliably find solutions even for problems whose natural merit functions have strict local minima that are not solutions. Based upon this strategy, three new algorithms are proposed for solving nonlinear mixed complementarity problems that represent a significant improvement in robustness over previous algorithms. These algorithms have local Qquadratic convergence behavior, yet depend only on a pseudomonotonicity assumption to achieve global convergence from arbitrary starting points. Using the MCPLIB and GAMSLIB test libraries, we perform extensive computational tests that demonstrate the effectiveness of these algorithms on realistic problems. Second, the thesis extends some previously existing algorithms to solve more general problem classes. Specifically, the NE/SQP method of Pang & Gabriel (1993), the semismooth equations approach of De Luca, Facchinei & Kanz...
A Semismooth Newton Method For Variational Inequalities: Theoretical Results And Preliminary Numerical Experience
, 1997
"... Variational inequalities over sets defined by systems of equalities and inequalities are considered. A continuously differentiable merit function is proposed whose unconstrained minima coincide with the KKTpoints of the variational inequality. A detailed study of its properties is carried out showi ..."
Abstract

Cited by 34 (11 self)
 Add to MetaCart
Variational inequalities over sets defined by systems of equalities and inequalities are considered. A continuously differentiable merit function is proposed whose unconstrained minima coincide with the KKTpoints of the variational inequality. A detailed study of its properties is carried out showing that under mild assumptions this reformulation possesses many desirable features. A simple algorithm is proposed for which it is possible to prove global convergence and a fast local convergence rate. Preliminary numerical results showing viability of the approach are reported.
NEOS and CONDOR: Solving Optimization Problems over the Internet
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1998
"... We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor ..."
Abstract

Cited by 34 (1 self)
 Add to MetaCart
We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations.
QPCOMP: A Quadratic Programming Based Solver for Mixed Complementarity Problems
 Mathematical Programming
, 1997
"... QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriel[14], this algorithm represents a significant advance in robustness at no cost in efficiency. In particular, th ..."
Abstract

Cited by 31 (15 self)
 Add to MetaCart
QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on the NE/SQP method of Pang and Gabriel[14], this algorithm represents a significant advance in robustness at no cost in efficiency. In particular, the algorithm is shown to solve any solvable Lipschitz continuous, continuously differentiable, pseudomonotone mixed nonlinear complementarity problem. QPCOMP also extends the NE/SQP method for the nonlinear complementarity problem to the more general mixed nonlinear complementarity problem. Computational results are provided, which demonstrate the effectiveness of the algorithm. 1 Introduction This paper describes a new algorithm for solving the mixed nonlinear complementarity problem (MCP), which provides a significant improvement in robustness over previous superlinearly or quadratically convergent algorithms, while preserving these fast local convergence properties. The MCP is defined in...
A nonsmooth inexact Newton method for the solution of largescale nonlinear complementarity problems
, 1997
"... A new algorithm for the solution of largescale nonlinear complementarity problems is introduced. The algorithm is based on a nonsmooth equation reformulation of the complementarity problem and on an inexact LevenbergMarquardttype algorithm for its solution. Under mild assumptions, and requiring o ..."
Abstract

Cited by 30 (5 self)
 Add to MetaCart
A new algorithm for the solution of largescale nonlinear complementarity problems is introduced. The algorithm is based on a nonsmooth equation reformulation of the complementarity problem and on an inexact LevenbergMarquardttype algorithm for its solution. Under mild assumptions, and requiring only the approximate solution of a linear system at each iteration, the algorithm is shown to be both globally and superlinearly convergent, even on degenerate problems. Numerical results for problems with up to 10000 variables are presented. 1 Introduction We consider the complementarity problem NCP(F ), which is to find a vector in IR n satisfying the conditions x 0; F (x) 0; x T F (x) = 0; where F : IR n ! IR n is a continuously differentiable function. Nonlinear complementarity problems have important applications, see, e.g., [11,19], which often call for the solution of largescale problems. During the last few years many methods have been developed for the solution of the non...