NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL MULTIOBJECTIVE PROBLEMS VIA CONVEXIFICATORS

Abstract

Many authors studied optimality conditions for vector optimization problems in recent years and obtained Kuhn-Tucker optimality conditions via Lagrange multipliers (see, e.g., Clarke (1983), Kuk, Lee and Tanino (2001), Liang, Huang and Pardalos (2001), Luc (2002),Gong (2010), Luu (2014, 2016), Gadhi (2015),...). Fritz John necessary optimality
conditions for fractional multiobjiective optimization problems with equality and inequality constraints which are assumed to be continuous but not necessarily Lipschitz are established. Under a constraint qualification of MangasarianFromovitz type, KuhnTucker
necessary optimality conditions for local weak efficient solutions are derived. In this paper, using results of Gadhi (2015), we derive necessary efficiency conditions via convexificators for fractional multi-objective problems with equality and inequality constraints which are
assumed to be continuous but not necessarily Lipschitz.