The usual duality results are established for mixed symmetric multiobjective dual programs without nonnegativity constraints using the notion of invexity/ generalized invexity which has allowed weakening various types of convexity/ generalized convexity assumptions. This mixed symmetric dual formulation unifies two existing symmetric dual formulations in the literature.

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...

First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the g...

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...

The purpose of this paper is to propose a method for approximating the solution split common fixed point problem involving \(\lambda\)-strict quasi-\(G_f\)-pseudocontractive mappings in setting two Banach spaces using \(G_f(.,.)\) functional. We prove that proposed converges strongly problem. In addition, we provide some applications our and numerical results demonstrate applicability method.

The main purpose of this paper is to study a pair of optimization problems on differentiable manifolds under (p, r)-invexity assumptions. By using the (p, r)-invexity assumptions on the functions involved, optimality conditions and duality results (Mond-Weir, Wolfe and mixed type) are established on differentiable manifolds. We construct counterexample to justify that our investigations are mor...

We consider a field F and positive integers n, m, such that m is not divisible by $$\mathrm {Char}(F)$$ prime to n!. The absolute Galois group $$G_F$$ acts on the $$\mathbb {U}_n(\mathbb {Z}/m)$$ of all $$(n+1)\times (n+1)$$ unipotent upper-triangular matrices over {Z}/m$$ cyclotomically. Given $$0,1\ne z\in F$$ an arbitrary list w n Kummer elements $$(z)_F$$ , $$(1-z)_F$$ in $$H^1(G_F,\mu _m)$...

The purpose of this paper is to consider a class of non-smooth multiobjective semi-infinite programming problem. Based on the concepts of local cone approximation, K − directional derivative and K − subdifferential, a new generalization of convexity, namely generalized uniform ( , , , ) K F d α ρ − − convexity, is defined for this problem. For such semi-infinite programming problem, several suf...

Sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the problems. It is pointed out that these results can be applied to the control problem with free boundary conditions and have linkage w...