On an exact penalty function method for semi-infinite programming problems

An exact penalty function for semi-infinite programming

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the g~ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result o...

An Exact Penalty Approach for Mixed Integer Nonlinear Programming Problems

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.

Optimality Conditions for Semi-infinite and Generalized Semi-infinite Programs via lp Exact Penalty Functions

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...

Penalty and Smoothing Methods for Convex Semi-Infinite Programming

In this paper we consider min-max convex semi-infinite programming. In order to solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences...

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