A Brief Review of Non-convex Single-Objective Optimization

Abstract

Single-objective optimization methods are among the mathematical methods most widely used in various applications. The classical methods starting with linear programming have been proved very valuable tools for solving various economic and engineering problems. However, the growing complexity of the applied problems demanded the development of new ideas, methods, and algorithms. The classical mathematical optimization methods are based on the assumption that an objective function is convex. The convexity assumption, which is very fruitful for theoretical investigation, is hardly provable in many practical applications. Moreover, it is not truth very frequently. Therefore in the 1960s of the last century there begun active research in global optimization of non-convex problems. Naturally, single-objective problems foremost attracted attention of researchers. In this section we briefly review the approaches to single-objective global optimization, the multi-objective counterparts of which are considered in subsequent chapters. For the comprehensive presentation we refer to the representative monographs.