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摘要
A semi-infinite programming (SIP) problem is an optimization problem which contains infinitely many constraints of finitely many variables. To solve the semi-infinite programming problem, a nonmonotone filter trust region method is proposed in this paper. By reformulating the Karush- Kuhn-Tucker system of a nonlinear programming, we obtain a system of semismooth equations that is equivalent to the SIP problem. Also, the NCP function is used to construct the semismooth equations. For solving this equivalent problem, a promising method, called filter method, is introduced. Compared with the existed methods for SIP, the presented method is more flexible and has several advantages as follows: first, the penalty function is not needed, which is widely used in algorithms for solving nonlinear equations. Second, to avoid the trial point from falling into the "valley", the non-monotonic technique is added into the method. Moreover, there is only one system of linear equations needed to be solved at per iteration. Additional, based on the ODE-type method, the proposed nonmonotone filter method is more flexible than other traditional methods. And the scale of calculation is reduced to a certain degree. Under some reasonable conditions, the global convergent properties of the presented method are proven.
- 出版日期2017-6
- 单位河北大学
