Math Prog Technical Reports
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Complementarity Problems in GAMS and the PATH Solver
(1998-09-25)A fundamental mathematical problem is to find a solution to a square system of nonlinear equations. There are many methods to approach this problem, the most famous of which is Newton's method. In this paper, we describe ... -
Mathematical Programming Approaches to Machine Learning and Data Mining
(1998)Machine learning problems of supervised classification, unsupervised clustering and parsimonious approximation are formulated as mathematical programs. The feature selection problem arising in the supervised classification ... -
Optimized Regional Caching for On-Demand Data Delivery
(1998)Systems for on-demand delivery of large, widely-shared data can use several techniques to improve cost/performance, including: multicast data delivery, segmented data delivery, and regional (or proxy) servers that cache ... -
Global Optimization Techniques for Mixed Complementarity Problems
(1998-07-30)We investigates the theoretical and numerical properties of two global optimization techniques for the solution of mixed complementarity problems. More precisely, using a standard semismooth Newton-type method as a basic ... -
k-Plane Clustering
(1998)A finite new algorithm is proposed for clustering m given points in n-dimensional real space into k clusters by generating k planes that constitute a local solution to the nonconvex problem of minimizing the sum of squares ... -
Optimizing the Delivery of Radiation Therapy to Cancer Patients
(1998)In the field of radiation therapy, much of the research is aimed at developing new innovative techniques for treating cancer patients with radiation. In recent years, new treatment machines have been developed that provide ... -
On the Identification of Zero Variables in an Interior-Point Framework
(1998-05-19)We consider column sufficient linear complementarity problems and study the problem of identifying those variables that are zero at a solution. To this end we propose a new, computationally inexpensive technique that is ... -
Massive Data Discrimination via Linear Suppot Vector Machines
(1999-03-31)A linear support vector machine formulation is used to generate a fast, finitely-terminating linear-programming algorithm for discriminating between two massive sets in n-dimensional space, where the number of points can ... -
Feature Selection Via Concave Minimization and Support Vector Machines
(1998)Computational comparison is made between two feature selection approaches for finding a separating plane that discriminates between two point sets in an n-dimensional feature space that utilizes as few of the n features ... -
Expressing Complementarity Problems in an Algebraic Modeling Language and Communicating Them to Solvers
(1998)Diverse problems in optimization, engineering, and economics have natural formulations in terms of complementarity conditions, which state (in their simplest form) that either a certain nonnegative variable must be zero ... -
Mathematical Programming for Data Mining: Formulations and Challenges
(1998)This paper is intended to serve as an overview of a rapidly emerging research and applications area. in addition to providing a general overview, motivating the importance of data mining problems within the area of knowledge ... -
A Hybrid Newton Method for Solving Box Constrained Variational Inequalitiy Problems Via the D-Gap Function
(1997-12-30)A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. A hybrid Netwon-type method is proposed for minimizing the D-gap function. Under ... -
A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems
(1997-12-30)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 ... -
Solving Box Constrained Variational Inequalities by Using the Natural Residual with D-Gap Function Globalization
(1997-11-21)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 ... -
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 ... -
Interfaces to PATH 3.0: Design, Implementation and Usage
(1998-05-05)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 ... -
Parsimonious Side Propagation
(1997)A fast parsimonious linear-programming-based 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 ... -
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 ... -
Modeliing Solution Environments for MPEC: GAMS & MATLAB
(1998-01)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 ... -
Jacobian Smoothing Methods for General Nonlinear Complementarity Problems
(1997-10-13)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 ...
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