Browsing Math Prog Technical Reports by Title
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Regularized Linear Programs with Equilibrium Constraints
(1997)We consider an arbitrary linear program with equilibrium constrains (LPEC) that may possibly be infeasible or have an unbounded objective function. We regularize the LPEC by perturbing it in a minimal way so that the ... 
Robust path choice in networks with failures
(1997)The problem of adaptive routing in a network with failures is considered. The network may be in one of finitely many states characterized by different travel times along the arcs, and transitions between the states occur ... 
ROBUST SOLUTION OF MIXED COMPLEMENTARITY PROBLEMS
(1994)This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem, or MCP. The MCP formulation is useful for expressing systems of nonlinear inequalities and equations; the ... 
The Semismooth Algorithm for Large Scale Complementarity Problems
(19990618)Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both ... 
Smooth Methods of Multipliers for Complementarity Problems
(199802)This paper describes several methods for solving nonlinear complementarity problems. A general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem., ... 
Smoothing Methods in Mathematical Programming
(1995)A class of parametric smooth functions that approximate the fundamental plus function, (x)+=max {0,x}, is obtained by twice integrating a probability density function. By means of this approximation, linear and convex ... 
Solution of General Linear Complemetarity Problems via nondifferentiable Concave Minimization
(1996)Finite termination, at point satisfying the minimum principle necessary optimality condition, is established for a stepless (no line search) successive linearization algorithm (SLA) for minimizing a nondifferentiable concave ... 
Solutions to Affine Generalized Equations Using Proximal Mappings
(199411)The normal map has proven to be a powerful tool for solving generalized equations of the form: find z ? C, with 0 ? F(z)+ Nc(z), where C is a convex set and Nc(z) is the normal cone to C at z. In this paper, we use the ... 
Solving Box Constrained Variational Inequalities by Using the Natural Residual with DGap Function Globalization
(19971121)We present a new method for the solution of the box constrained variational inequality problem, BVIP for short. Basically, this method is a nonsmooth Newton method applied to a reformulation of BVIP as a system of nonsmooth ... 
STABILITY PROPERTIES OF THE GRADIENT PROJECTION METHOD WITH APPLICATIONS TO THE BACKPROPAGATION ALGORITHM
(19940606)Convergence properties of the generalized gradient projection algorithm in the presence of data perturbations are investigated. It is shown that every trajectory of the method is attracted, in a certain sense, to an ... 
Synchronous and Asynchronous MultiCoordination Method for the Solution of BlockAngular Programs
(1996)Several types of multicoordination methods for blockangular programs are considered. We present a computational comparison of synchronous multicoordination methods. The most efficient of these approaches is shown to ... 
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems
(19971230)In this paper we introduce a general line search scheme which easily allows us to define and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic ... 
Traffic Modeling and Variational Inequalities using GAMS
(199704)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 ... 
A variablepenalty alternating directions method for convex optimization
(1995)We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each ...