Optimality Analysis of a Class of Semi-infinite Programming Problems

Autor:	Lin Chen, Ka Fai Cedric Yiu, Fei Chen, Zhi Guo Feng
Rok vydání:	2020
Předmět:	Sequence Control and Optimization Optimization problem Series (mathematics) Applied Mathematics Theory of computation Fixed-point theorem Applied mathematics Monotonic function Limit (mathematics) Management Science and Operations Research Semi-infinite programming Mathematics
Zdroj:	Journal of Optimization Theory and Applications. 186:398-411
ISSN:	1573-2878 0022-3239
DOI:	10.1007/s10957-020-01708-8
Popis:	In this paper, we consider a class of semi-infinite programming problems with a parameter. As the parameter increases, we prove that the optimal values decrease monotonically. Moreover, the limit of the sequence of optimal values exists as the parameter tends to infinity. In finding the limit, we decompose the original optimization problem into a series of subproblems. By calculating the maximum optimal values to the subproblems and applying a fixed-point theorem, we prove that the obtained maximum value is exactly the limit of the sequence of optimal values under certain conditions. As a result, the limit can be obtained efficiently by solving a series of simplified subproblems. Numerical examples are provided to verify the limit obtained by the proposed method.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::460c70969d35a049d4f12f1571413916 https://doi.org/10.1007/s10957-020-01708-8 Zobrazit plný text záznamu Full text from SpringerLink