Contractibility of the solution sets in strictly quasiconcave vector maximization on noncompact domains.
https://doi.org/10.1007/s10957-004-1177-9Publisher, magazine: ,
Publication year: 2005
Lưu Trích dẫn Chia sẻAbstract
We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of \textit{J. Benoist} [J. Optimization Theory Appl. 110, No. 2, 325–336 (2001; Zbl 1009.90101)], which was established for problems on compact feasible domains.
Tags: Vector optimization; strictly quasiconcave functions; noncompact feasible domains; efficient solution sets; contractibility
Các bài viết liên quan đến tác giả Nguyễn Quang Huy
Remarks on a conjecture of J. Benoist
Global minimization of difference of quadratic and convex functions over box or binary constraints
Unbounded components in the solution sets of strictly quasiconcave vector maximization problems
Global optimality of quadratic minimization over symmetric polytopes
Kuhn-Tucker sufficiency for global minimum of multi-extremal mathematical programming problems
On the Contractibility of the Efficient and Weakly Efficient Sets in R2