Painlevé–Kuratowski convergence of the solution sets for controlled systems of fuzzy vector quasi-optimization problems with application to controlling traffic networks under uncertainty

2021 ◽  
Vol 40 (1) ◽  
Author(s):  
Nguyen Van Hung ◽  
André A. Keller
Keyword(s):  
Optimization Problems ◽  
Traffic Networks ◽  
Solution Sets ◽  
Controlled Systems ◽  
Kuratowski Convergence ◽  
Fuzzy Vector

External and internal stability in set optimization using gamma convergence

2019 ◽  
Vol 35 (3) ◽  
pp. 393-406
Author(s):  
C. S. LALITHA ◽  
◽  
Keyword(s):  
Optimization Problems ◽  
Image Space ◽  
Set Optimization ◽  
Internal Stability ◽  
Gamma Convergence ◽  
Decision Space ◽  
Solution Sets ◽  
Stability Of Solution ◽  
Kuratowski Convergence ◽  
The Stability

The main objective of this paper is to investigate the stability of solution sets of perturbed set optimization problems in the decision space as well as in the image space, by perturbing the objective maps. For a sequence of set-valued maps, a notion of gamma convergence is introduced to establish the external and internal stability in terms of Painlev´e–Kuratowski convergence of sequence of solution sets of perturbed problems under certain compactness assumptions and domination properties.

scholarly journals On solution sets of nonconvex Darboux problems and applications to optimal control with endpoint constraints

1996 ◽  
Vol 37 (3) ◽  
pp. 354-391 ◽  
Author(s):  
H. D. Tuan
Keyword(s):  
Constraint Qualification ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Regularity Assumption ◽  
Darboux Problem ◽  
Continuous Version ◽  
Open Mapping Theorem ◽  
Solution Sets ◽  
Relaxation Theorem ◽  
Endpoint Constraints

AbstractWe prove a continuous version of a relaxation theorem for the nonconvex Darboux problem xlt ε F(t, τ, x, xt, xτ). This result allows us to use Warga's open mapping theorem for deriving necessary conditions in the form of a maximum principle for optimization problems with endpoint constraints. Neither constraint qualification nor regularity assumption is supposed.

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.

Evaluating solution sets of a posteriori solution techniques for bi-criteria combinatorial optimization problems

2005 ◽  
Vol 8 (1) ◽  
pp. 75-96 ◽  
Author(s):  
John W. Fowler ◽  
Bosun Kim ◽  
W. Matthew Carlyle ◽  
Esma Senturk Gel ◽  
Shwu-Min Horng
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
A Posteriori ◽  
Solution Sets ◽  
Combinatorial Optimization Problems ◽  
Solution Techniques

Convergence of Subdifferentials of Convexly Composite Functions

1999 ◽  
Vol 51 (2) ◽  
pp. 250-265 ◽  
Author(s):  
C. Combari ◽  
R. Poliquin ◽  
L. Thibault
Keyword(s):  
Banach Space ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Second Order ◽  
Constrained Optimization Problems ◽  
Composite Functions ◽  
Kuratowski Convergence ◽  
General Banach Space

AbstractIn this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.

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