The Auxiliary Function Method For Nonlinear Global Optimization

Global optimization problem is a broad used discipline， which constructscomputing approaches to find the optimal solution and study the theory andapplication value, the theoretical and practical value of these methods so that managerdiscusses the characters of optimal choice on decision problems. Methods for solvingglobal optimization are effectively applied in most of problems such as sciencetechnology, engineering design, economics and management. Research on globaloptimization has made rapid progress recently. Now it has developed into anindependent branch in the optimization field. In recent decades many new approachesfor global optimization have been proposed，such as interval method,integral-level setmethod,the tunneling function method and the filled function method. The filledfunction method and tunneling function method is to realize the process of solving theglobal optimal solution by using an auxiliary transform function, so we refer to themas the auxiliary function method. The core content of this paper is the auxiliaryfunction method for nonlinear global optimization.The paper is organized as follows: In the first chapter, some basic concepts andcharacters of general nonlinear programming are introduced．Then some approachesfor solving global optimization problems are briefly presented．In the second chapter,A new definition of filled function method for global discrete optimization whichfuction in paper [29] is modified and a corresponding filled function is constructed.What’s more， we design an algorithm and get the numerical results. In the thirdchapter, A new modified T-F function algorithm forRnconstrained globaloptimization is proposed and it is proved that this new modified T-F function has twoproperties of tunneling function and filled function. We design an algorithm accordingto the modified T-F function and we explore the application of this modified T-Ffunction method with supply chain. It shows that the algorithm is effectiveConclusions and recommendations are drawn in final chapter.