On Quasidifferentiable Multiobjective Fractional Programming

On quasidifferentiable mathematical programs with equilibrium constraints

“…Some stationary conditions [44] for the QMPEC are extended under quasidifferentiabiity. The notion of generalized convexity introduced by Singh and Laha [41] which unifies the functions introduced by Antczak [2] and by Nobakhtian [38] has been used to explore the criteria under which a 𝑊−stationary point becomes a global (or a local) minimizer of the QMPEC. Further, some other constraint qualifications and stationary conditions [16,18,22,36,44] under different generalized convexity assumptions [26,34,35,42] can be investigated for the QMPEC.…”

“…Based on the notion of 𝐹−convex functions wrt convex compact set given by Antczak [2, Definition 4.2] and generalized (𝐹, 𝜌)−convexity given by Nobakhtian [38], Singh and Laha [41] gave the following notions of generalized 𝐹− convexity in terms of convex compact set. The following theorem gives a sufficient condition for a weak stationary point of the QMPEC to be optimal.…”

“…Baier et al [4] looked at directed and Rubinov subdifferentials of quasidifferentiable functions. Some recent interesting results in the field of quasidifferentiable programming is due to Antczak [2,3], Abbasov [1], Dolgopolik [12,13], Lin et al [27], Singh and Laha [41,42] which have induced further scope of study.…”

Second-order Optimality Conditions for Nonsmooth Multiobjective Fractional Optimization Problems

“…When the objective function in a multiobjective optimization problem is represented by fractional formulae, the problem is said to be multiobjective fractional optimization problem. Recently, optimality conditions and dual theorems of multiobjective fractional optimization problems are popular in the field of optimization theories, see [4][5][6][7][8][9][10][11][12][13]. Ojha [4] considered a pair of second-order symmetric duals in the context of nondifferentiable multiobjective fractional programming problems.…”

“…Ojha [4] considered a pair of second-order symmetric duals in the context of nondifferentiable multiobjective fractional programming problems. Singh [5] dealt with a class of multiobjective fractional programs involving quasidifferentiable functions and derived necessary and sufficient optimality conditions for efficiency of this problem. Tripathy [6] introduced three approaches of mixed type multiobjective fractional dual programming and the weak and strong duality theorems.…”