Generalized logarithmic penalty function method for solving smooth nonlinear programming involving invex functions

An objective penalty function method for nonlinear programming

K e y w o r d s N o n l i n e a r programming, Exact penalty function, Objective penalty function. 1. I N T R O D U C T I O N The problem we consider in this paper is as follows: f0(x), s.t. k ( a ) < 0, i E I = { 1 , 2 , . . . , m } , (P) The authors would like to thank anonymous referees' comments and remarks that help us to improve the presentation of this paper considerably. This research w...

A logarithmic barrier function method for solving nonlinear multiobjective programming problems

Abstract: An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton m...

The l1 exact G-penalty function method and G-invex mathematical programming problems

Nonlinear programming without a penalty function

Abstract. In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the co...

Exact Penalty Functions for Nonlinear Integer Programming Problems

Abstract In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a...