scholarly journals On sequential optimality conditions for smooth constrained optimization

Optimization ◽  
2011 ◽  
Vol 60 (5) ◽  
pp. 627-641 ◽  
Author(s):  
Roberto Andreani ◽  
Gabriel Haeser ◽  
J. M. Martínez
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Sequential Optimality Conditions

scholarly journals Sequential optimality conditions for cardinality-constrained optimization problems with applications

2021 ◽  
Author(s):  
Christian Kanzow ◽  
Andreas B. Raharja ◽  
Alexandra Schwartz
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Optimality Condition ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Local Minimizer ◽  
Constrained Optimization Problems ◽  
New Approach ◽  
Mathematical Programs ◽  
Sequential Optimality Conditions

AbstractRecently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka–Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.

scholarly journals On sequential optimality conditions for smooth constrained optimization

Optimization ◽  
2011 ◽  
Vol 60 (8-9) ◽  
pp. 1119-1119
Author(s):  
Roberto Andreani ◽  
Gabriel Haeser ◽  
J.M. Martínez
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Sequential Optimality Conditions

scholarly journals Strong complementary approximate Karush-Kuhn-Tucker conditions for multiobjective optimization problems

2021 ◽  
pp. 24-24
Author(s):  
Jitendra Maurya ◽  
Shashi Mishra
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
Multiobjective Optimization Problems ◽  
Sequential Optimality Conditions ◽  
Equality And Inequality Constraints ◽  
Optim Theory

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications and introduce a weak constraint qualification which assures the equivalence between SCAKKT and the strong Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483{500, 1994) conditions for multiobjective optimization problems.

Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization

2018 ◽  
Vol 43 (3) ◽  
pp. 693-717 ◽  
Author(s):  
Roberto Andreani ◽  
José Mario Martínez ◽  
Alberto Ramos ◽  
Paulo J. S. Silva
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Constraint Qualifications ◽  
Sequential Optimality Conditions
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