| Title:
|
Existence of minimizers and necessary conditions in set-valued optimization with equilibrium constraints (English) |
| Author:
|
Bao, Truong Q. |
| Author:
|
Mordukhovich, Boris S. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
52 |
| Issue:
|
6 |
| Year:
|
2007 |
| Pages:
|
453-472 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form \[ 0\in G(x)+Q(x), \] where both $G$ and $Q$ are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the Palais-Smale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation. (English) |
| Keyword:
|
variational analysis |
| Keyword:
|
nonsmooth and set-valued optimization |
| Keyword:
|
equilibrium constraints |
| Keyword:
|
existence of optimal solutions |
| Keyword:
|
necessary optimality conditions |
| Keyword:
|
generalized differentiation |
| MSC:
|
49J52 |
| MSC:
|
49J53 |
| MSC:
|
90C29 |
| MSC:
|
90C30 |
| MSC:
|
90C33 |
| idZBL:
|
Zbl 1164.49306 |
| idMR:
|
MR2357575 |
| DOI:
|
10.1007/s10492-007-0027-0 |
| . |
| Date available:
|
2009-09-22T18:31:21Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134690 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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