Abstract
In this paper we apply the directional derivative technique to characterize D-multifunction, quasi D-multifunction and use them to obtain ε-optimality for set valued vector optimization problem with multivalued maps. We introduce the notions of local and partial-ε-minimum (weak) point and study ε-optimality, ε-Lagrangian multiplier theorem and ε-duality results.
Highlights
The theory of efficiency plays an important role in various knowledge fields
We introduce the notions of local and partial-ε-minimum point and study ε-optimality, ε-Lagrangian multiplier theorem and ε-duality results
The notion of proper efficiency was first introduced by Kuhn and Tucker [1] in their well known paper on nonlinear programming and many other notions have been proposed since
Summary
The theory of efficiency plays an important role in various knowledge fields. It is proposed as a new frontier in mathematical physics and engineering in context of priorities concerning the alternative energies, the climate exchange and education. Chinaie and Zafarani [6] introduced the concepts of feeble multifunction minimum (weak) point, multifunction minimum (weak) point and obtained optimality conditions for set valued vector optimization problem having multivalued objective and constraints. Chinaie and Zafarani [9] introduced the concepts of ε-feeble multifunction minimum (weak) point and obtained optimality conditions for set valued vector optimization problem having multivalued objective and constraints. We have given the notions of (local) partial-ε-minimum point and (local) partial-ε-weak minimum point, for set valued vector optimization problem and used them to study ε-optimality, ε-Lagrangian multiplier theorem and ε-duality results.
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