EXPONENTIAL METHODS FOR CONVEX PROGRAMMING UNDER LINEAR EQUATION CONSTRAINTS

Abstract

The barrier and penalty functions methods are one of the Lagrangian multiplier methods for solving both constrained nonlinear equation and optimization problems. In this paper we introduce a new method called exponential method to solve optimization problem on convex function under linear constraints. It presents some variety of the method. The global behavior of this method will be given. Theorems and algorithms for the method are also given in this paper. The main result of this method as follows; that is, every penalty (barrier) parameters value that converging to infinity, the exponential penalty (barrier) function has unique minimizer (maximizer), respectively. And then, the sequence of the minimizers (maximizers), will converge to the minimizer of the original problem.

Keywords: Exponential penalty, convex programming, Linear equation constraints.