Filled Function Method For Solving The Global Optimization Of Nonlinear Programming

To find the effective methods for finding the global optimal solutions of a general multi-minimizers function is one of the hot topics. There are two difficulties in global optimization: One is how to leave from a local minimizer to a smaller one and the other is how to judge the current minimizer is global. The filled function algorithm introduced is one of the well-known and practical methods for settling the first difficulty. In recent years, many kinds of filled functions with parameters have been presented. However, those parameters are too hard to adjust and it is most probable .that global optimizers are lost or fake better minimizers are found. Therefore, Further research is worthy of continuing on how we can construct filled functions with simple forms. Better properties and algorithms are more efficient.The main work summarized as follows:In chapter one, some methods for global optimization problems are briefly presented. Including the new filled function methods, the interval algorithm, the modified tunneling methods and the integral function methods; and so on.In chapter two, a new filled function with one parameter is suggested for finding a global minimum point for a general class of nonlinear programming problems with a closed bounded domain .Without the Lipschitz continuous condition, a new algorithm is presented according to the theoretical analysis. The implementation of the algorithms on several test problems is reported with satisfactory numerical results.In chapter three, a novel filled function with one parameter is suggested in this paper for finding a global minimum point for a general class of nonlinear programming problem with a closed bounded domain .The implementation of the algorithms on several test problems is reported with satisfactory numerical results.In chapter four , a new auxiliary function with one parameter with box constrained on R nfor escaping the current local minimum point of global optimization problem is proposed .Under some mild assumptions,we prove it is a filled function .A new algorithm is presented according to the theoretic analysis .And some numerical results demonstrate the efficiency of this g1obal method for unconstrained g1obal optimization.