Duality Theory And Numerical Solution For Semi-infinite Programming

Semi-infinite programming is studied from two aspects in this thesis.On the one hand,in theory,we study the duality theory of semi-infinite programming.First,for the invex and Higher-order(?,?)-V-invex semi-infinite programming,taking Wolfe-type dual and MondWeir-type dual as examples respectively,the weak,strong and strict converse duality theorems are established.Then,taking Lagrange-type dual as an example,the duality theory of nonconvex semi-infinite programming problem is discussed,a new augmented Lagrangian function is constructed.Under reasonable assumptions,the strong duality theorem between the primal problem and the augmented Lagrangian dual problem holds.Finally,an example is given to verify the presented results.On the other hand,in the numerical method,a non-monotonic augmented Lagrangian filter method is proposed.Firstly,the semi-infinite programming problem is discretized.Then,combining the basic augmented Lagrangian method with the modified non-monotone filter technique,we employ filter to control the optimality measure and constraint violation.We also include a feasibility restoration phase that allows fast detection of infeasible problems.Compared with the existing methods,our method is more flexible and avoids the Maratos effect to a certain degree by using a non-monotonic filter technique.Finally,numerical experiment are given to illustrate the effectiveness of the algorithm.