Name
Title | ||
|---|---|---|
Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems |
Abstract | ||
|---|---|---|
Let (P) denote the vector maximization problem $$\max\{f(x)=\big(f_1(x),\ldots,f_m(x)\big){:}\,x\in D\},$$ where the objective functions f i are strictly quasiconcave and continuous on the feasible domain D, which is a closed and convex subset of R n . We prove that if the efficient solution set E(P) of (P) is closed, disconnected, and it has finitely many (connected) components, then all the components are unbounded. A similar fact is also valid for the weakly efficient solution set E w (P) of (P). Especially, if f i (i=1,...,m) are linear fractional functions and D is a polyhedral convex set, then each component of E w (P) must be unbounded whenever E w (P) is disconnected. From the results and a result of Choo and Atkins [J. Optim. Theory Appl. 36, 203---220 (1982.)] it follows that the number of components in the efficient solution set of a bicriteria linear fractional vector optimization problem cannot exceed the number of unbounded pseudo-faces of D. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10898-006-9032-1 | J. Global Optimization |
Keywords | Field | DocType |
Strictly quasiconcave vector maximization problem,Efficient solution set,Weakly efficient solution set,Unbounded component,compactification procedure,90C29,90C26 | Discrete mathematics,Combinatorics,Mathematical optimization,Vector optimization,Vector maximization,Quasiconvex function,Convex set,Regular polygon,Solution set,Mathematics | Journal |
Volume | Issue | ISSN |
37 | 1 | 0925-5001 |
Citations | PageRank | References |
2 | 0.38 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| T. N. Hoa | 1 | 2 | 0.38 |
| N. Q. Huy | 2 | 47 | 5.11 |
| T. D. Phuong | 3 | 2 | 0.38 |
| N. D. Yen | 4 | 104 | 17.57 |