On Constraint Dropping Schemes and Optimality Functions for a Class of Outer Approximations Algorithms

Abstract

This paper presents a new class of outer approximations algorithms which incorporate constraint dropping schemes. The algorithms are based on the use of certain types of optimality functions, which are commonly used in minimization algorithms, for defining stationary points. The algorithms are implementable in that all the inner minimizations and maximizations need to be carried out only approximately. It is shown that any accumulation point constructed by these algorithms is both feasible and stationary.