scholarly journals Some Convexificators-Based Optimality Conditions for Nonsmooth Mathematical Program with Vanishing Constraints

2021 ◽  
Vol 11 (06) ◽  
pp. 324-337
Author(s):  
Qingjie Hu ◽  
Zhijuan Zhou ◽  
Yu Chen
Keyword(s):  
Optimality Conditions ◽  
Mathematical Program ◽  
Vanishing Constraints

scholarly journals Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR ◽  
2021 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Smooth Vector ◽  
Duality Results ◽  
Vanishing Constraints ◽  
Multiobjective Programming Problems

AbstractIn this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

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