Browsing Math Prog Technical Reports by Title
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Parsimonious Least Norm Approximation
(1997)A theoretically justifiable fast finite successive linear approximation algorithm is proposed for obtaining a parsimonious solution to a corrupted linear system Ax=b+p, where the corruption p is due to noise or error in ... 
Parsimonious Side Propagation
(1997)A fast parsimonious linearprogrammingbased algorithm for training neural networks is proposed that suppresses redundant features while using a minimal number of hidden units. This is achieved by propagating sideways to ... 
A Pathsearch Damped Newton Method for Computing General Equilibria
(199404)Computable general equilibrium models and other types of variational inequalities play a key role in computational economics. This paper describes the design and implementation of a pathsearchdamped Newton method for ... 
Polyhedral Boundary Projection
(1997)We consider the problem of projecting a point in a polyhedral set onto the boundary of the set using an arbitrary norm for the projection. Two types of polyhedral sets, one defined by a convex combination of k points in ... 
Preprocessing Complementarity Problems
(1999)Preprocessing techniques are extensively used by linear and integer programming communities as a means to improve model formulation by reducing size and complexity. Adaptations and extension of these methods for use within ... 
Projection Support Vector Machines
(2000)Largescale classification is a very active research line in data mining. It can be applied to problems like credit card fraud detection or contentbased document browsing. In recent years, several efficient algorithms for ... 
QPCOMP: A Quadratic Programming Based Solver for Mixed Complementarity Problems
(19960207)QPCOMP is an extremely robust algorithm for solving mixed nonlinear complementarity problems that has fast local convergence behavior. Based in part on NE/SQP method of Pang and Gabriel [14], this algorithm represents a ... 
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 ...