scholarly journals Optimality conditions for a bilevel optimization problem in terms of KKT multipliers and convexificators

2019 ◽  
Vol 10 (2) ◽  
pp. 329-335
Author(s):  
Nazih Abderrazzak Gadhi ◽  
◽  
Lahoussine Lafhim ◽  
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Bilevel Optimization

scholarly journals SOLUTION OF THE LARGE MINIMUM COMPLIANCE PROBLEM USING BILEVEL OPTIMIZATION

2016 ◽  
Vol 12 (2) ◽  
pp. 5928-5937
Author(s):  
Makrizi Abdelilah ◽  
Bouchaïb Radi
Keyword(s):  
Topology Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Numerical Results ◽  
Topology Optimization Problem ◽  
Single Level ◽  
Minimum Compliance ◽  
Bilevel Problem ◽  
Compliance Problem

The topology optimization problem have a great industrial interest. Using the subdomains method, we have formulated the decomposed topology optimization problem as a bilevel one. In this paper, we reformulate our bilevel problem as a single level optimization problem by replacing the lower level optimization problem with its KKT optimality conditions, we give also a new algorithm and numerical results.

Derivatives of Hadamard type in vector optimization

2018 ◽  
Vol 68 (2) ◽  
pp. 421-430
Author(s):  
Karel Pastor
Keyword(s):  
Nonlinear Analysis ◽  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimality Condition ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Dini Derivatives ◽  
Scalar Optimality ◽  
Derivatives Of

Abstract In our paper we will continue the comparison which was started by Vsevolod I. Ivanov [Nonlinear Analysis 125 (2015), 270–289], where he compared scalar optimality conditions stated in terms of Hadamard derivatives for arbitrary functions and those which was stated for ℓ-stable functions in terms of Dini derivatives. We will study the vector optimization problem and we show that also in this case the optimality condition stated in terms of Hadamard derivatives is more advantageous.

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