Proper Efficiency and Generalized Convexity in Nonsmooth Vector Optimization Problems

Lecture Notes in Economics and Mathematical Systems - Generalized Convexity and Generalized Monotonicity ◽

10.1007/978-3-642-56645-5_14 ◽

2001 ◽

pp. 208-217 ◽

Cited By ~ 3

Author(s):

Giorgio Giorgi ◽

Angelo Guerraggio

Keyword(s):

Vector Optimization ◽

Generalized Convexity ◽

Optimization Problems ◽

Proper Efficiency ◽

Vector Optimization Problems ◽

Nonsmooth Vector Optimization

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Exponential type vector variational-like inequalities and nonsmooth vector optimization problems

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-014-0828-8 ◽

2014 ◽

Vol 49 (1-2) ◽

pp. 127-143 ◽

Cited By ~ 2

Author(s):

Anurag Jayswal ◽

Sarita Choudhury

Keyword(s):

Vector Optimization ◽

Exponential Type ◽

Optimization Problems ◽

Vector Optimization Problems ◽

Nonsmooth Vector Optimization

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Generalized vector variational-like inequalities and nonsmooth vector optimization problems

Optimization ◽

10.1080/02331934.2010.538056 ◽

2012 ◽

Vol 61 (9) ◽

pp. 1075-1086 ◽

Cited By ~ 9

Author(s):

Xian-Jun Long ◽

Jian-Wen Peng ◽

Soon-Yi Wu

Keyword(s):

Vector Optimization ◽

Optimization Problems ◽

Vector Optimization Problems ◽

Nonsmooth Vector Optimization

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Some vector optimization problems in Banach spaces with generalized convexity

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2007.05.002 ◽

2007 ◽

Vol 54 (11-12) ◽

pp. 1403-1410 ◽

Cited By ~ 9

Author(s):

Guolin Yu ◽

Sanyang Liu

Keyword(s):

Banach Spaces ◽

Vector Optimization ◽

Generalized Convexity ◽

Optimization Problems ◽

Vector Optimization Problems

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Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID=""ID="" This research was partially supported by the National Natural Science Foundation of P.R. China and the Natural Science Foundation of Jiangxi Province, P.R. China.

Mathematical Methods of Operations Research ◽

10.1007/pl00003994 ◽

2000 ◽

Vol 51 (3) ◽

pp. 443-457 ◽

Cited By ~ 14

Author(s):

Wei Liu ◽

Xunhua Gong

Keyword(s):

Vector Optimization ◽

Natural Science ◽

Optimization Problems ◽

Proper Efficiency ◽

Vector Optimization Problems ◽

Jiangxi Province

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On the Applications of Nonsmooth Vector Optimization Problems to Solve Generalized Vector Variational Inequalities Using Convexificators

Advances in Intelligent Systems and Computing - Optimization of Complex Systems: Theory, Models, Algorithms and Applications ◽

10.1007/978-3-030-21803-4_66 ◽

2019 ◽

pp. 660-671 ◽

Cited By ~ 1

Author(s):

Balendu Bhooshan Upadhyay ◽

Priyanka Mishra ◽

Ram N. Mohapatra ◽

Shashi Kant Mishra

Keyword(s):

Variational Inequalities ◽

Vector Optimization ◽

Optimization Problems ◽

Vector Variational Inequalities ◽

Vector Optimization Problems ◽

Generalized Vector Variational Inequalities ◽

Nonsmooth Vector Optimization

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Nonsmooth Vector Optimization Problems

Lecture Notes in Economics and Mathematical Systems - Theory of Vector Optimization ◽

10.1007/978-3-642-50280-4_3 ◽

1989 ◽

pp. 62-79 ◽

Cited By ~ 6

Author(s):

Dinh The Luc

Keyword(s):

Vector Optimization ◽

Optimization Problems ◽

Vector Optimization Problems ◽

Nonsmooth Vector Optimization

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Isolated minimizers and proper efficiency for C0,1 constrained vector optimization problems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2005.01.041 ◽

2005 ◽

Vol 309 (1) ◽

pp. 353-368 ◽

Cited By ~ 19

Author(s):

Ivan Ginchev ◽

Angelo Guerraggio ◽

Matteo Rocca

Keyword(s):

Vector Optimization ◽

Optimization Problems ◽

Proper Efficiency ◽

Vector Optimization Problems ◽

Isolated Minimizers

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Optimality conditions and duality results for a new class of nonconvex nonsmooth vector optimization problems

Miskolc Mathematical Notes ◽

10.18514/mmn.2021.2780 ◽

2021 ◽

Vol 22 (1) ◽

pp. 49

Author(s):

Tadeusz Antczak ◽

Ram Verma

Keyword(s):

Optimality Conditions ◽

Vector Optimization ◽

Optimization Problems ◽

Vector Optimization Problems ◽

New Class ◽

Duality Results ◽

Nonsmooth Vector Optimization

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On Minty variational principle for nonsmooth vector optimization problems with generalized approximate convexity

Optimization ◽

10.1080/02331934.2018.1466884 ◽

2018 ◽

Vol 67 (8) ◽

pp. 1157-1167 ◽

Cited By ~ 1

Author(s):

Pooja Gupta ◽

S. K. Mishra

Keyword(s):

Variational Principle ◽

Vector Optimization ◽

Optimization Problems ◽

Vector Optimization Problems ◽

Approximate Convexity ◽

Nonsmooth Vector Optimization

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NECESSARY OPTIMALITY CONDITIONS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2003.9637221 ◽

2003 ◽

Vol 8 (2) ◽

pp. 165-174 ◽

Cited By ~ 1

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.

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