# Optimality conditions for weak $${\psi}$$ -sharp minima in vector optimization problems

Optimality conditions for weak $${\psi}$$ -sharp minima in vector optimization problems In this paper, we develop the characterization of weak $${\psi}$$ -sharp minimizer by means of an oriented distance function and investigate the weak $${\psi}$$ -sharp minimizer of the composition of two functions. Moreover, we establish sufficient conditions of the weak $${\psi_1}$$ -sharp and $${\psi_2}$$ -sharp Pareto minimality for vector optimization problem with strictly differentiable and twice strictly differentiable objective function, respectively. Our results extend the corresponding ones in the literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Optimality conditions for weak $${\psi}$$ -sharp minima in vector optimization problems

, Volume 17 (3) – May 9, 2012
8 pages

/lp/springer_journal/optimality-conditions-for-weak-psi-sharp-minima-in-vector-optimization-edQtg4M52U
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0182-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we develop the characterization of weak $${\psi}$$ -sharp minimizer by means of an oriented distance function and investigate the weak $${\psi}$$ -sharp minimizer of the composition of two functions. Moreover, we establish sufficient conditions of the weak $${\psi_1}$$ -sharp and $${\psi_2}$$ -sharp Pareto minimality for vector optimization problem with strictly differentiable and twice strictly differentiable objective function, respectively. Our results extend the corresponding ones in the literature.

### Journal

PositivitySpringer Journals

Published: May 9, 2012

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