On sufficiency and duality theorems for nonsmooth semi-infinite mathematical programming problem with equilibrium constraints

2021 ◽  
Author(s):  
Tran Van Su ◽  
Dinh Dieu Hang
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Mathematical Programming Problem ◽  
Equilibrium Constraints ◽  
Duality Theorems

scholarly journals Multiobjective Interaction Programming Problem with Interaction Constraint for Two Players

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Min Jiang ◽  
Zhiqing Meng ◽  
Xinsheng Xu ◽  
Rui Shen ◽  
Gengui Zhou
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Programming Model ◽  
Weight Vector ◽  
Mathematical Programming Problem ◽  
Pricing Model ◽  
Multi Objective ◽  
Joint Solution ◽  
Joint Pricing ◽  
Better Than

This paper extends an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents). First, we define ans-optimal joint solution with weight vector to multi-objective interaction programming problem with interaction constraint for two players and get some properties of it. It is proved that thes-optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Then, we define anothers-optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties. It is proved that thes-optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain. Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.

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