Algorithm Analysis Of Two Kinds Of Constrained Optimization Problems

In this paper,different algorithms are designed for two kinds of constrained optimization problems.For semi-infinite programming,we present a new unified penalty function method,which contains some previous penalty function types as special cases.The main theorem demonstrates that the penalty function is exact under the mangasarian-fromovitz constraint qualification conditions.More precise-ly,when the penalty parameter is large enough,the local optimal solution of the penalty problem converges to the one of the original problem.In addition,two ex-amples of linear-phase FIR digital filter design and PID controller design often yield good results in numerical experiments.For nonsubmodular maximization under a knapsack constraint,a satisfactory approximation algorithm is designed.Firstly,we relax the original problem and employ the continuous greedy algorithm to acquire a fractional solution of the new problem;then the contention solution scheme is applied to make the fractional solution feasible.