scholarly journals Sequential optimality conditions for convex optimization

2019 ◽  
Author(s):  
K. Jeyalakshmi ◽  
K. Poornima
Keyword(s):  
Convex Optimization ◽  
Optimality Conditions ◽  
Sequential Optimality Conditions

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

A CONVEX SUBMODEL WITH APPLICATION TO SYSTEM DESIGN

2004 ◽  
Vol 21 (01) ◽  
pp. 9-33
Author(s):  
JAVIER SALMERÓN ◽  
ÁNGEL MARÍN
Keyword(s):  
Convex Optimization ◽  
System Design ◽  
Optimality Conditions ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Lagrangean Relaxation ◽  
Optimization Techniques ◽  
Convex Model ◽  
Design Problems ◽  
Primal And Dual

In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve large design problems in facility location and capacity expansion. To attain the optimal solution of the model, we analyze its Karush–Kuhn–Tucker optimality conditions and develop a constructive algorithm that provides the optimal primal and dual solutions. This approach yields better performance than other convex optimization techniques.

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.

Optimality conditions in convex optimization revisited

2011 ◽  
Vol 7 (2) ◽  
pp. 221-229 ◽  
Author(s):  
Joydeep Dutta ◽  
C. S. Lalitha
Keyword(s):  
Convex Optimization ◽  
Optimality Conditions
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