The Research On Penalty-Function-Free Methods For Semi-Infinite Programming

Semi-infinite programming(SIP)arise in many fields,such as control of robots,eigenvalue computations,electric power system and so on,it focus on infinite decision variables or constrained functions.Semi-infinite programming was proposed in 1924,and then developed into an independent branch of optimization theory in 1980.There are two main topics for general semi-infinite programming in this paper.On one hand,a modified filter trust region method is proposed.Firstly,SIP is transformed into a finite optimization problem by discretization method.Secondly,we obtain the search direction and trial points by combining trust region method and modified sequential quadratic programming(SQP)method.Then combining the trust region method and filter technique,whether the trial point is accepted by filter or not is judged,so that the selection of penalty factor in penalty function and the Maratos effect is avoided to a certain degree.On the other hand,we present a non-monotone adaptive method for general SIP.We transform the SIP into a finite programming using the integral method,combining penalty function method,trust region method and SQP method,we construct quadratic subproblem of finite problem to obtain search directions and trial point.The self-adaptive multiplier is considered in the construction of quadratic subproblem.Then together with the non-monotonic strategies,the flexible acceptance criteria of trial point according to the improvement of objective function or constraint violation function is established,and modified non-monotone adaptive method for SIP is obtained.In each iteration,motivated by the filter technique,we construct a balance of the objective function and the constraint violation function and the Maratos effect is avoided to a certain degree.In the end,the numerical results show that the proposed algorithm is effective.