Coordinate -Turning And Searching Method And Intercepting Hypersurface Method For Global Optimization

Lots of practical problems exist in science, engineering, economy, finance, military affairs and so on. There are many local minimizers in these problems. The traditional algorithms for local optimization can get the local minimizers, but difficult to get the global minimizer. Therefore, solving the global optimization problems has been the mainstreem in the fields of mathematical programming in recent twenty, thirty years, and it becomes a hot topic in the research of optimization. Some typical methods have been proposed one after the other by many researchers recently. As a whole, however, theories for global optimization have not yet been completed, still need further improved and enrichment.On the base of plentiful work by former researchers, two new methods are proposed in the paper. Illumined by RM (Rosenbrock Method) and FFM (Filled Function Method), the first method, which is called CTSM (Coordinate-Turning and Searching Method), is proposed. FFM is one of the most effective deterministic methods for global optimization. FFM contains some iterative times and two phases included in a time. Lots of effective filled functions which are used in FFM for global minimization have been proposed up to now. But many filled functions contain parameters. There are no parameter-selecting theories and results for different kinds of objective functions present. RM is one of the traditional methods which directly search minimizers. Its strategy is searching the next downhill direction and constructing a new series of Coordinates not by solving the derivative but by comparing the values of the function advantages. Although its basic thoughts can be easily understood and algorithm realizes conveniently among the deterministic methods, the speed of searching is a little slow. The paper combines the advantages as well as avoids their disadvantages of the two methods to give a new strategy and a new method.Illumined by TM (tunneling algorithm), the second method, which is called IHM (Intercepting-Hypersurface Method), is proposed. TM is also one of the most effective deterministic methods for global optimization. It is Like FFM which uses the local minimization algorithms. But it needs selecting parameters of tunneling function and this causes much trouble, such as increasing the quantity of computing, the complexity of the tunneling function etc. Replacing"tunneling"in the tunneling algorithm, CASM"jumps"over the present basin into a lower basin by solving an intercepting-hypersurface equation. Then an amended algorithm is proposed as some disadvantage contained in IHM.The structure of the paper is as below. Chapter 1 and chapter 2 are the foreword of the paper. A brief introduction is given to the methods for global optimization in chapter 1. In chapter 2, several direct algorithms for local optimization are briefly introduced, then FFM and TM are described in detail. Thereinto, some representative filled functions are listed and analyzed.The main body of the paper is chapter 3 and chapter 4. In chapter 3, (CASA) Coordinate-Attempting and Searching Strategy is given to us and then CASM is formed on the base of CASA. Theories and analysis about CASM are provided. The paper provides many numerical experiments to prove the effectiveness of the algorithm.In chapter 4, another intercepting-hypersurface strategy based on solving the intercepting-hypersurface equation is proposed. Then paper provides and analyzes interrelated theories in detail about the strategy. The algorithm is also described concretely. In the end, a lot of numerical experiments show the algorithm is effective.To some extent, our work broadens the idea and strategy for global minimization and enriches methods for global minimization.