Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems

2019 ◽  
Vol 36 (04) ◽  
pp. 1950021
Author(s):  
Tijani Amahroq ◽  
Abdessamad Oussarhan
Keyword(s):  
Optimality Conditions ◽  
Lagrange Multiplier ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Set Optimization ◽  
Vector Equilibrium Problems ◽  
Multiplier Rules ◽  
Convexity Assumption ◽  
Vector Equilibrium ◽  
Weak Vector

Optimality conditions are established in terms of Lagrange–Fritz–John multipliers as well as Lagrange–Kuhn–Tucker multipliers for set optimization problems (without any convexity assumption) by using new scalarization techniques. Additionally, we indicate how these results may be applied to some particular weak vector equilibrium problems.

scholarly journals A Note on Continuity of Solution Set for Parametric Weak Vector Equilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Pakkapon Preechasilp ◽  
Rabian Wangkeeree
Keyword(s):  
Equilibrium Problem ◽  
Vector Optimization ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problem ◽  
Vector Optimization Problems ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Weak Vector

We consider the parametric weak vector equilibrium problem. By using a weaker assumption of Peng and Chang (2014), the sufficient conditions for continuity of the solution mappings to a parametric weak vector equilibrium problem are established. Examples are provided to illustrate the essentialness of imposed assumptions. As advantages of the results, we derive the continuity of solution mappings for vector optimization problems.

scholarly journals LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 85-95 ◽  
Author(s):  
SHENG-JIE LI ◽  
HUI-MIN LIU ◽  
CHUN-RONG CHEN
Keyword(s):  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problems ◽  
Solution Mapping ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

scholarly journals An Approximation Theorem for Vector Equilibrium Problems under Bounded Rationality

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 45
Author(s):  
Wensheng Jia ◽  
Xiaoling Qiu ◽  
Dingtao Peng
Keyword(s):  
Exact Solution ◽  
Bounded Rationality ◽  
Equilibrium Problems ◽  
Approximation Theorem ◽  
Optimization Problems ◽  
Vector Equilibrium Problems ◽  
Special Cases ◽  
Full Rationality ◽  
Vector Equilibrium ◽  
Special Case

In this paper, our purpose is to investigate the vector equilibrium problem of whether the approximate solution representing bounded rationality can converge to the exact solution representing complete rationality. An approximation theorem is proved for vector equilibrium problems under some general assumptions. It is also shown that the bounded rationality is an approximate way to achieve the full rationality. As a special case, we obtain some corollaries for scalar equilibrium problems. Moreover, we obtain a generic convergence theorem of the solutions of strictly-quasi-monotone vector equilibrium problems according to Baire’s theorems. As applications, we investigate vector variational inequality problems, vector optimization problems and Nash equilibrium problems of multi-objective games as special cases.

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