Deterministic methods in constrained global optimization: Some recent advances and new fields of application

Abstract

Recent developments in deterministic global optimization methods have considerably enlarged the fields of optimization where those methods can be successfully applied. It is the purpose of the present article to give a brief survey of both some of the most promising methods and new fields of application. The methods considered comprise branch and bound and outer approximation as well as combinations of branch and bound with outer approximation. The fields of applications to be discussed include concave minimization, reverse convex programming, d.c. programming, Lipschitzian optimization, systems of equations, and (or) inequalities and global integer programming.

A one-parameter filled function for nonsmooth global optimization and its application

“…The situation is similar to the stopping criteria. Generally speaking, the methods of global optimization can be divided into two types: Stochastic methods such as those in [1][2][3], and deterministic methods such as those in [4][5][6][7].…”

A FFACGO for Constrained Global Optimization

“…In comparison with other methods devoted to solve constrained global optimization problems with special structural property [4,[6][7][8], FFACGO appears to have several advantages over them mainly due to its wide application in solving constrained global optimization problems without special structural property and its relatively easy actualization with a process that aims at finding better minima. This paper focuses on the FFACGO.…”

Solving variational inequalities defined on a domain with infinitely many linear constraints

“…The methods of Kelley-Cheney-Goldstein [3,17], Veinott [27], and Elzinga-Moore [5] were widely applied and modified in various manners [4,16,25,26]. A recent development is using analytic center based cutting plane methods to solve variational inequalities [8,12,[20][21][22][23].…”