Multiobjective symmetric duality involving cones

Higher order optimality and duality in fractional vector optimization over cones

“…Proceeding on the lines of Lemma 1 given by Suneja et al [21] we have the following Fritz-John type necessary optimality conditions for a point to be a weak minimum of (FP).…”

Second-Order Symmetric Duality in Multiobjective Programming Over Cones

“…Since (x,ȳ,λ,p) is an efficient solution for (MP), by the Fritz-John necessary optimality conditions [14], there exist α ∈ K * , β ∈ C 2 , γ ∈ R + , such that the following conditions are satisfied at (x,ȳ,λ,p) (for simplicity, we write…”

Nondifferentiable multiobjective Mond–Weir type second-order symmetric duality over cones

“…Definition 2.2 [15,25] A pointx ∈ X o is an efficient solution of (P1) if there exists no x ∈ X o such that f (x) − f (x) ∈ K \{0}.…”

“…Proof Since (x,ȳ,λ,z,p) is an efficient solution for (MP), by the Fritz John necessary optimality conditions [25], there exist α ∈ K * , β ∈ C 2 , γ ∈ R + such that the following conditions are satisfied at (x,ȳ,λ,z,p) (for simplicity, we write ∇…”

“…Remark 3.1 To prove the above theorem, we have used Fritz John necessary optimality conditions [25], for which the constraints x ∈ C 1 and v ∈ C 2 are required. However, if all the cones (K , C 1 and C 2 ) are non-negative orthants, then one can use Fritz John necessary conditions [21], wherein the constraints x 0 and v 0 are not needed.…”