Filled Function Methods For Solving Bilevel Programming Problems And Constrained Optimization Problems

As an effective deterministic method for solving global optimization problems,the filled function methods have attracted many scholars' attention.This thesis mainly discusses the application of the filled function methods to solve bi-level programming problems and constrained optimization problems.First of all,for the bi-level programming problem with equality and inequality constraints,this thesis uses the KKT condition of the lower problem to transform bi-level programming into a single-level constraint programming problem;combined with the penalty function,according to the definition of the filled function,A new filled function is constructed and its properties are discussed;based on the constructed filled function,a filled function method for solving bi-level programming problems is proposed.two numerical examples are used to verify the feasibility and effectiveness of the algorithm.Secondly,for optimization problems with equality and inequality constraints,a new filled function is constructed,and its properties are discussed.The constructed filled function is continuously differentiable and contains neither exponential terms nor logarithmic terms;based on the constructed new filled function,a filled function method for solving constrained optimization problems is proposed.Finally,two numerical examples are used to verify the feasibility of the algorithm.Finally,the research work of this thesis is summarized,and further prospects for future research directions are made.