Entropic Perturbation Approach to Mathematical Programming

Abstract

The barrier and penalty function methods for solving mathematical programming problems have been widely used for both theoretical and computational purposes. In a penalty approach, any point outside of the feasible region is assigned a penalty while, in a barrier approach, those feasible solutions near the boundary of the feasible region are subject to a penalty. Both approaches are designed to prevent the search process for an optimal solution from wondering away from the feasible region. They can be considered as an objective-perturbation approach. This chapter studies the objective-perturbation approach by using the entropic function, \(\sum {_j x_j \ln x_j } \) for solving four classes of problems, namely, linear programming problems in Karmarkar’s form, linear programming programs in standard form, convex quadratic programming problems, and linear and convex quadratic semi-infinite programming problems.