Density and connectedness of optimal points with respect to improvement sets

Optimization ◽  
2021 ◽  
pp. 1-30
Author(s):  
Yu Han
Keyword(s):  
Improvement Sets

Existence and Convergence of Optimal Points with Respect to Improvement Sets

2016 ◽  
Vol 26 (2) ◽  
pp. 1293-1311 ◽  
Author(s):  
Pirro Oppezzi ◽  
Anna Rossi
Keyword(s):  
Improvement Sets

Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

2020 ◽  
Vol 37 (04) ◽  
pp. 2040003
Author(s):  
Zai-Yun Peng ◽  
Jing-Jing Wang ◽  
Xian-Jun Long ◽  
Fu-Ping Liu
Keyword(s):  
Efficient Solution ◽  
Sufficient Conditions ◽  
Quasi Equilibrium ◽  
Nonlinear Scalarization ◽  
Solution Sets ◽  
Improvement Sets ◽  
Oriented Distance ◽  
Kuratowski Convergence ◽  
Symmetric Set ◽  
Convergence Of Solution

This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)[Formula: see text] via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)[Formula: see text] are obtained through a new nonlinear scalarization technical. Then, under [Formula: see text]-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)[Formula: see text] is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)[Formula: see text] under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

Improvement Sets and Convergence of Optimal Points

2014 ◽  
Vol 165 (2) ◽  
pp. 405-419 ◽  
Author(s):  
Pirro Oppezzi ◽  
Anna Rossi
Keyword(s):  
Improvement Sets

Existence of Optimal Points Via Improvement Sets

2015 ◽  
Vol 167 (2) ◽  
pp. 487-501 ◽  
Author(s):  
Maurizio Chicco ◽  
Anna Rossi
Keyword(s):  
Improvement Sets

Characterizations of improvement sets via quasi interior and applications in vector optimization

2015 ◽  
Vol 10 (4) ◽  
pp. 769-780 ◽  
Author(s):  
Yuan Mei Xia ◽  
Wan Li Zhang ◽  
Ke Quan Zhao
Keyword(s):  
Vector Optimization ◽  
Improvement Sets ◽  
Quasi Interior

Vector Optimization Problems via Improvement Sets

2011 ◽  
Vol 150 (3) ◽  
pp. 516-529 ◽  
Author(s):  
M. Chicco ◽  
F. Mignanego ◽  
L. Pusillo ◽  
S. Tijs
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Improvement Sets
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