Global Minimization of Nonsmooth Constrained Global Optimization with Filled Function

Wei-Xiang Wang,You-Lin Shang,Ying Zhang

doi:10.1155/2014/563860

Abstract

A novel filled function is constructed to locate a global optimizer or an approximate global optimizer of smooth or nonsmooth constrained global minimization problems. The constructed filled function contains only one parameter which can be easily adjusted during the minimization. The theoretical properties of the filled function are discussed and a corresponding solution algorithm is proposed. The solution algorithm comprises two phases: local minimization and filling. The first phase minimizes the original problem and obtains one of its local optimizers, while the second phase minimizes the constructed filled function and identifies a better initial point for the first phase. Some preliminary numerical results are also reported.

Highlights

Science and economics rely on the increasing demand for locating the global optimization optimizer, and global optimization has become one of the most attractive research areas in optimization
Global optimization methods can be divided into two categories: stochastic methods and deterministic methods
In practice, optimization problems may be nonsmooth and often have many complicated constraints and the number of local minimizers may be infinite. To deal with such situation, in this paper, we extend filled function methods to the case of nonsmooth constrained global optimization and propose a new filled function

Summary

Introduction

Science and economics rely on the increasing demand for locating the global optimization optimizer, and global optimization has become one of the most attractive research areas in optimization. The stochastic methods are usually probability based approaches, such as genetic algorithm and simulated annealing method These stochastic methods have their advantages, but their shortages are obvious, such as being trapped in a local optimizer. The filled function approach, initially proposed for smooth optimization by Ge and Qin [4] and improved in [5,6,7], is one of the effective global optimization approaches It furnishes us with an efficient way to use any local optimization procedure to solve global optimization problem. In practice, optimization problems may be nonsmooth and often have many complicated constraints and the number of local minimizers may be infinite To deal with such situation, in this paper, we extend filled function methods to the case of nonsmooth constrained global optimization and propose a new filled function. The interior, the boundary, and the closure of the set S are denoted by int S, ∂S, and clS, respectively

A New One-Parameter Filled Function and Its Properties

Filled Function Algorithm FFAM

Conclusion