scholarly journals NECESSARY OPTIMALITY CONDITIONS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS

2003 ◽  
Vol 8 (2) ◽  
pp. 165-174 ◽  
Author(s):  
Davide La Torre
Keyword(s):  
Optimality Conditions ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Clarke Subdifferential ◽  
Vector Optimization Problems ◽  
Generalized Derivative ◽  
Nonsmooth Vector Optimization ◽  
Vector Case ◽  
The Clarke Subdifferential

In this paper we introduce a notion of generalized derivative for nonsmooth vector functions in order to obtain necessary optimality conditions for vector optimization problems. This definition generalizes to the vector case the notion introduced by Michel and Penot and extended by Yang and Jeyakumar. This generalized derivative is contained in the Clarke subdifferential and then the corresponding optimality conditions are sharper than the Clarke's ones.

scholarly journals Generalized Nonsmooth Exponential-Type Vector Variational-Like Inequalities and Nonsmooth Vector Optimization Problems in Asplund Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 345
Author(s):  
Syed Shakaib Irfan ◽  
Mijanur Rahaman ◽  
Iqbal Ahmad ◽  
Rais Ahmad ◽  
Saddam Husain
Keyword(s):  
Vector Optimization ◽  
Exponential Type ◽  
Optimization Problems ◽  
Existence Of Solution ◽  
Vector Optimization Problems ◽  
Limiting Subdifferential ◽  
Kkm Theorem ◽  
Nonsmooth Vector Optimization ◽  
Asplund Spaces ◽  
Mordukhovich Limiting Subdifferential

The aim of this article is to study new types of generalized nonsmooth exponential type vector variational-like inequality problems involving Mordukhovich limiting subdifferential operator. We establish some relationships between generalized nonsmooth exponential type vector variational-like inequality problems and vector optimization problems under some invexity assumptions. The celebrated Fan-KKM theorem is used to obtain the existence of solution of generalized nonsmooth exponential-type vector variational like inequality problems. In support of our main result, some examples are given. Our results presented in this article improve, extend, and generalize some known results offer in the literature.

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