Second-order necessary optimality conditions for domain optimization problems of the Neumann type

1990 ◽  
Vol 65 (3) ◽  
pp. 431-445 ◽  
Author(s):  
Y. Goto ◽  
N. Fujii ◽  
Y. Muramatsu
Keyword(s):  
Optimality Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Second Order ◽  
Domain Optimization ◽  
Neumann Type

A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems

2018 ◽  
Vol 52 (2) ◽  
pp. 567-575 ◽  
Author(s):  
Do Sang Kim ◽  
Nguyen Van Tuyen
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Smooth Vector ◽  
Incorrect Result

The aim of this note is to present some second-order Karush–Kuhn–Tucker necessary optimality conditions for vector optimization problems, which modify the incorrect result in ((10), Thm. 3.2).

New second-order radial epiderivatives and applications to optimality conditions

2020 ◽  
Vol 54 (4) ◽  
pp. 949-959
Author(s):  
Xiaoyan Zhang ◽  
Qilin Wang
Keyword(s):  
Optimality Conditions ◽  
Recent Literature ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Contingent Epiderivative ◽  
Proper Efficient Solutions

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.

scholarly journals Minimum Principle-Type Necessary Optimality Conditions in Scalar and Vector Optimization. An Account

2017 ◽  
Vol 9 (4) ◽  
pp. 168
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Minimum Principle ◽  
Necessary Optimality Conditions ◽  
Equality Constraints ◽  
Vector Optimization Problems ◽  
Scalar Optimization ◽  
Scalar And Vector Optimization

We take into condideration necessary optimality conditions of minimum principle-type, that is for optimization problems having, besides the usual inequality and/or equality constraints, a set constraint. The first part pf the paper is concerned with scalar optimization problems; the second part of the paper deals with vector optimization problems.

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