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.

scholarly journals First-Order Optimality Conditions in Multiobjective Optimization Problems: Differentiable Case

1970 ◽  
Vol 29 ◽  
pp. 99-105 ◽  
Author(s):  
MM Rizvi ◽  
Muhammad Hanif ◽  
GM Waliullah
Keyword(s):  
Multiobjective Optimization ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Multiobjective Optimization Problems ◽  
Equality And Inequality Constraints ◽  
Vector Valued ◽  
Type Constraint

T. Maeda gave some constraint qualifications to get positive Lagrange multipliers associated with the vector-valued objective function and under these conditions, he derived Karush-Kuhn-Tucker (KKT) type necessary conditions for inequality constraints. In this paper, we have defined these Maeda-type constraint qualifications under different sets and have derived KKT type necessary conditions for both equality and inequality constraints. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 29 (2009) 99-105  DOI: http://dx.doi.org/10.3329/ganit.v29i0.8519

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

scholarly journals A Novel Hybrid Algorithm for Solving Multiobjective Optimization Problems with Engineering Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Lulu Fan ◽  
Tatsuo Yoshino ◽  
Tao Xu ◽  
Ye Lin ◽  
Huan Liu
Keyword(s):  
Multiobjective Optimization ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Primary Energy ◽  
Engineering Practice ◽  
Optimization Strategy ◽  
Frontal Collision ◽  
Multiobjective Optimization Problems ◽  
Crashworthiness Design

An effective hybrid algorithm is proposed for solving multiobjective optimization engineering problems with inequality constraints. The weighted sum technique and BFGS quasi-Newton’s method are combined to determine a descent search direction for solving multiobjective optimization problems. To improve the computational efficiency and maintain rapid convergence, a cautious BFGS iterative format is utilized to approximate the Hessian matrices of the objective functions instead of evaluating them exactly. The effectiveness of the proposed algorithm is demonstrated through a comparison study, which is based on numerical examples. Meanwhile, we propose an effective multiobjective optimization strategy based on the algorithm in conjunction with the surrogate model method. This proposed strategy has been applied to the crashworthiness design of the primary energy absorption device’s crash box structure and front rail under low-speed frontal collision. The optimal results demonstrate that the proposed methodology is promising in solving multiobjective optimization problems in engineering practice.

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