A new exact penalty method for semi-infinite programming problems

作者：Lin Qun^*; Loxton Ryan; Teo Kok Lay; Wu Yong Hong; Yu Changjun

来源：Journal of Computational and Applied Mathematics, 2014, 261: 271-286.

DOI：10.1016/j.cam.2013.11.010

• Exact penalty function
• Semi-infinite programming
• Constrained optimization
• Nonlinear programming

In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design.

• 出版日期2014-5-1