Second order modified objective function method for twice differentiable vector optimization problems over cone constraints

Anurag Jayswala; Tadeusz Antczakb; Shalini Jha

doi:10.3934/naco.2019010

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2019, Volume 9, Issue 2: 133-145. Doi: 10.3934/naco.2019010

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Second order modified objective function method for twice differentiable vector optimization problems over cone constraints

a.
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India
b.
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland

^* Corresponding author: Shalini Jha, Visiting Scientist, Machine Intelligence Unit (MIU), Indian Statistical Institute (ISI) Kolkata, India - 700108
^* Corresponding author: Shalini Jha, Visiting Scientist, Machine Intelligence Unit (MIU), Indian Statistical Institute (ISI) Kolkata, India - 700108

Received: January 2017

Revised: August 2018

Published: January 2019

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Abstract

In the paper, a vector optimization problem with twice differentiable functions and cone constraints is considered. The second order modified objective function method is used for solving such a multiobjective programming problem. In this method, for the considered twice differentiable multi-criteria optimization problem, its associated second order vector optimization problem with the modified objective function is constructed at the given arbitrary feasible solution. Then, the equivalence between the sets of (weakly) efficient solutions in the original twice differentiable vector optimization problem with cone constraints and its associated modified vector optimization problem is established. Further, the relationship between an (weakly) efficient solution in the original vector optimization problem and a saddle-point of the second order Lagrange function defined for the modified vector optimization problem is also analyzed.

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Mathematics Subject Classification: Primary: 90C26, 90C29, 90C46; Secondary: 90C25.

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