Browsing Math Prog Technical Reports by Issue Date
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Fast EquiPartitioning of Rectangular Domains using Stripe Decomposition
(19960205)This paper presents a fast algorithm that provides optimal or near optimal solutions to the minimum perimeter problem on a rectangular grid. The minimum perimeter problem is to partition a grid of size MxN into P equal ... 
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 ... 
Error Bounds for Nondifferentiable Convex Inequalities under a Strong Slater Constraint Qualification
(199607)A global error bound is given on the distance between an arbitrary point in the ndimensional real space R^n and its projection on a nonempty convex set determined by m convex, possibly nondifferentiable, inequalities. The ... 
Operator Splitting Methods for Monotone Affine Variational Inequalities, with Parallel Application to Optimal Control
(19960730)This paper applies splitting techniques developed for setvalued maximal monotone operators to monotone affine variational inequalities, including as a special case the classical linear complementarity problem. We give a ... 
The Linear Convergence of a Successive Linear Programming Algorithm
(19961203)We present a successive linear programming algorithm for solving constrained nonlinear optimization problems. The algorithm employs an Armijo procedure for updating a trust region radius. We prove the linear convergence ... 
Improved Generalization via Tolerant Training
(19961220)Theoretical and computational justification is given for improved generalization when the training set is learned with less accuracy. The model used for this investigation is a simple linear one. It is shown that learning ... 
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 ... 
ArbitraryNorm Separating Plane
(1997)A plane separating two point sets in ndimensional real space is constructed such that it minimized the sum of arbitrarynorm distances of misclassified points to the plane. In contrast the previous approaches used surrogates ... 
MinimumSupport Solutions of Polyhedral Concave Programs
(1997)Motivated by the successful application of mathematical programming techniques to difficult machine learning problems, we seek solutions of concave minimization problems over polyhedral sets with a minimum number of nonzero ... 
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 ... 
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 ... 
MinimumPerimeter Domain Assignment
(1997)For certain classes of problems defined over twodimensional domains with grid structure, optimization problems involving the assignment of grid cells to processors present a nonlinear network model for the problem of ... 
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 ... 
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 ... 
Feature Selection via Mathematic Programming
(199704)The problem of discriminating between two finite point sets in ndimensional feature space by a separating plane that utilizes as few of the features as possible, is formulated as a mathematical program with a parametric ... 
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 ... 
Jacobian Smoothing Methods for General Nonlinear Complementarity Problems
(19971013)We present a new algorithm for the solution of general (not necessarily monotone) complementarity problems. The algorithm is based on a reformulation of the complementarity problem as a nonsmooth system of equations by ... 
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 ... 
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 ... 
A Hybrid Newton Method for Solving Box Constrained Variational Inequalitiy Problems Via the DGap Function
(19971230)A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the Dgap function. A hybrid Netwontype method is proposed for minimizing the Dgap function. Under ...