An Exact Penalty Approach for Mixed Integer Nonlinear Programming Problems

Roohollah Aliakbari Shandiz,Nezam Mahdavi-Amiri

doi:10.4236/ajor.2011.13021

Abstract

We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.

Highlights

One way for relaxing the integer constraints on the variables of a problem is adding an appropriate penalty term to the objective function to create a new problem with only continuous variables
We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables
We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems

Summary

Introduction

One way for relaxing the integer constraints on the variables of a problem is adding an appropriate penalty term to the objective function to create a new problem with only continuous variables. This approach was first introduced by Ragavachari [1] to solve 0-1 linear programming problems and was used by several researchers for solving real nonlinear discrete programming problems [2,3,4,5]. In [7], the exact penalty approach was extended to nonlinear integer programming problems. We extend the exact penalty approach to constrained mixed integer nonlinear programming problems.

Penalty Method for Unconstrained MINLP Problems

Exact Penalty Functions

Extension to Constrained Problems

Summary