Numerical solutions of nonlinear programming problems with inequality constraints by reformulation

Abstract

The purpose of this paper is to give a new reformulation for nonlinear programming problems with inequality constraints which enables us to better use numerical techniques to obtain solutions. We show that the critical point conditions of our reformulated problems are equivalent to the classical first order necessary conditions which are usually used to obtain a minimizing solution. In particular, we convert the original inequality problems to an equality problem with auxiliary slack variables so that existing numerical techniques such as Newton's method can be used to solve these problems.