The Optimality Condition of Henig Proper Efficiency for a Set-Valued Optimization Problem

2016 ◽  
Author(s):  
Wang Haiying ◽  
Fu Zufeng
Keyword(s):  
Optimality Condition ◽  
Optimization Problem ◽  
Proper Efficiency ◽  
Henig Proper Efficiency

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.

scholarly journals Necessary optimality condition for trilevel optimization problem

2020 ◽  
Vol 16 (1) ◽  
pp. 55-70
Author(s):  
Gaoxi Li ◽  
◽  
Zhongping Wan ◽  
Jia-wei Chen ◽  
Xiaoke Zhao ◽  
...  
Keyword(s):  
Optimality Condition ◽  
Optimization Problem ◽  
Necessary Optimality Condition

scholarly journals A New Sequential Optimality Condition of Cardinality-Constrained Optimization Problem and Application

2021 ◽  
Author(s):  
Liping Pang ◽  
Menglong Xue ◽  
Na Xu
Keyword(s):  
Constrained Optimization ◽  
Optimality Condition ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Accumulation Point ◽  
Iterative Sequence ◽  
Stationary Points ◽  
Constrained Optimization Problem ◽  
Cardinality Constraint ◽  
Continuous Relaxation

Abstract In this paper, we consider the cardinality-constrained optimization problem and propose a new sequential optimality condition for the continuous relaxation reformulation which is popular recently. It is stronger than the existing results and is still a first-order necessity condition for the cardinality constraint problem without any additional assumptions. Meanwhile, we provide a problem-tailored weaker constraint qualification, which can guarantee that new sequential conditions are Mordukhovich-type stationary points. On the other hand, we improve the theoretical results of the augmented Lagrangian algorithm. Under the same condition as the existing results, we prove that any feasible accumulation point of the iterative sequence generated by the algorithm satisfies the new sequence optimality condition. Furthermore, the algorithm can converge to the Mordukhovich-type (essentially strong) stationary point if the problem-tailored constraint qualification is satisfied.

scholarly journals Approximate proper efficiency for multiobjective optimization problems

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6091-6101
Author(s):  
Ying Gao ◽  
Zhihui Xu
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problem ◽  
Normal Cone ◽  
Generalized Convexity ◽  
Optimization Problems ◽  
Proper Efficiency ◽  
Proximal Normal Cone ◽  
Radiant Set ◽  
Benson Proper Efficiency ◽  
Multiobjective Optimization Problems

This paper is devoted to the study of a new kind of approximate proper efficiency in terms of proximal normal cone and co-radiant set for multiobjective optimization problem. We derive some properties of the new approximate proper efficiency and discuss the relations with the existing approximate concepts, such as approximate efficiency and approximate Benson proper efficiency. At last, we study the linear scalarizations for the new approximate proper efficiency under the generalized convexity assumption and give some examples to illustrate the main results.

scholarly journals A duality theorem for a multiple objective fractional optimization problem

1986 ◽  
Vol 34 (3) ◽  
pp. 415-425 ◽  
Author(s):  
T. Weir
Keyword(s):  
Duality Theorem ◽  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Proper Efficiency ◽  
Dual Solution ◽  
Multiple Objective ◽  
Fractional Optimization ◽  
Linear Problems

Characterizations of efficiency and proper efficiency are given for classes of multiple objective fractional optimization problems. These results are then applied to the case of multiple objective fractional linear problems. A dual problem is given for the multiple objective fractional problem and it is shown that for a properly efficient primal solution the dual solution is also properly efficient.

AN OPTIMALITY CONDITION FOR THE ASSEMBLY DISTRIBUTION IN A NUCLEAR REACTOR

2005 ◽  
Vol 15 (03) ◽  
pp. 407-435 ◽  
Author(s):  
LAURENT THEVENOT
Keyword(s):  
Spectral Theory ◽  
Optimality Condition ◽  
Design Parameter ◽  
Optimization Problem ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Reactor Core ◽  
Homogenization Method ◽  
Transport Models ◽  
Multigroup Neutron

This paper presents an optimality condition for the optimization problem of the assembly distribution in a nuclear reactor, by using the homogenization method. In this paper the reactivity of the reactor core is measured by the critical eigenvalue for both continuous and multigroup neutron transport models. In particular, we extend the spectral theory of the critical eigenvalue and prove the differentiability of the latter with respect to the design parameter, the configuration of the fuels.

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