Results 1 
7 of
7
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.
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints
 SIAM Journal on Optimization
, 1997
"... Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the ex ..."
Abstract

Cited by 35 (0 self)
 Add to MetaCart
Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations. We present two globally convergent algorithms based on sequential quadratic programming, SQP, as applied in exact penalty methods for nonlinear programs. Global convergence of the implicit smooth SQP method depends on existence of a lowerlevel nondegenerate (strictly complementary) limit point of the iteration sequence. Global convergence of the explicit smooth SQP method depends on a weaker property, i.e. existence of a limit point at which a generalized constraint qualification holds. We also discuss some practical matter...
QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints
"... . We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) co ..."
Abstract

Cited by 20 (5 self)
 Add to MetaCart
. We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, firstlevel constraints are linear, and secondlevel (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, illconditioning, convexity of the objective, monotonicity and symmetry of the secondlevel problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.maths.mu.OZ.AU/~danny/qpecgendoc.h...
Traffic Modeling and Variational Inequalities using GAMS
 Operations Research and Decision Aid Methodologies in Traffic and Transportation Management, NATO ASI Series F
, 1997
"... We describe how several traffic assignment and design problems can be formulated within the GAMS modeling language using newly developed modeling and interface tools. The fundamental problem is user equilibrium, where multiple drivers compete noncooperatively for the resources of the traffic network ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
We describe how several traffic assignment and design problems can be formulated within the GAMS modeling language using newly developed modeling and interface tools. The fundamental problem is user equilibrium, where multiple drivers compete noncooperatively for the resources of the traffic network. A description of how these models can be written as complementarity problems, variational inequalities, mathematical programs with equilibrium constraints, or stochastic linear programs is given. At least one general purpose solution technique for each model format is briefly outlined. Some observations relating to particular model solutions are drawn. 1 Introduction Models that postulate ways to assign traffic within a transportation network for a given demand have been used in planning and analysis for many years, see [41] and references therein. A popular technique for such assignment is to use the shortest path between the origin and destination points of a given journey. Of course, s...
Modeling and Solution Environments for MPEC: GAMS
 Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods
, 1998
"... We describe several new tools for modeling MPEC problems that are built around the introduction of an MPEC model type into the GAMS language. We develop subroutines that allow such models to be communicated directly to MPEC solvers. This library of interface routines, written in the C language, prov ..."
Abstract
 Add to MetaCart
We describe several new tools for modeling MPEC problems that are built around the introduction of an MPEC model type into the GAMS language. We develop subroutines that allow such models to be communicated directly to MPEC solvers. This library of interface routines, written in the C language, provides algorithmic developers with access to relevant problem data, including for example, function and Jacobian evaluations. A MATLAB interface to the GAMS MPEC model type has been designed using the interface routines. Existing MPEC models from the literature have been written in GAMS, and computational results are given that were obtained using all the tools described. Keywords Complementarity, Algorithm, MPEC, Modeling 1 Introduction The Mathematical Program with Equilibrium Constraints (MPEC) arises when one seeks to optimize an objective function subject to equilibrium contraints. These equilibrium constraints may take the form of a variational inequality or complementarity problem, o...
A Globally Convergent Sequential Linear Programming Algorithm for Mathematical Programs with Linear Complementarity Constraints 1
"... Abstract: This paper presents a sequential linear programming algorithm for computing a stationary point of a mathematical program with linear equilibrium constraints. The algorithm is based on a formulation of equilibrium constraints as a system of semismooth equations by means of a perturbed Fishe ..."
Abstract
 Add to MetaCart
Abstract: This paper presents a sequential linear programming algorithm for computing a stationary point of a mathematical program with linear equilibrium constraints. The algorithm is based on a formulation of equilibrium constraints as a system of semismooth equations by means of a perturbed FisherBurmeister functional. Using only data of the problem, we introduce a method to update the parameter that characterizes the aforesaid perturbed functional. Some computational results are reported.