A Unified Tool for Solving Uni-Parametric Linear Programs, Convex Quadratic Programs, and Linear Complementarity Problems

TL;DR

This paper presents a unified method for efficiently solving uni-parametric linear, quadratic, and complementarity problems, demonstrating its effectiveness through small-scale examples and initial computational tests.

Contribution

The paper introduces a novel unified technique capable of solving various uni-parametric optimization problems, extending applicability across multiple problem types.

Findings

Method successfully solves small-scale examples

Initial computational tests show promise for larger problems

Unified approach simplifies solving diverse problem classes

Abstract

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We demonstrate the use of our method on a small, motivating example and present the results of a small number of computational tests demonstrating its utility for larger scale problems.