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The paper studies the second-order interval-valued variational problem under $$\eta $$ -bonvexity assumptions and proves the necessary optimality conditions. We investigate the functional which is $$\eta $$ -bonvex but not invex. Further, we prove the duality theorems i.e. the weak and strong duality theorem to relate the values of the primal problem and dual problem. To validate the credibility of the weak duality theorem, we formulate an example of a second-order interval-valued variational problem.

We aim to establish sufficient optimality conditions in terms of $$\text{ GA }$$ -stationary vectors and construct Wolfe and Mond–Weir types dual model in terms of contingent epiderivatives for the global optimal solution of nonsmooth semi-infinite mathematical programming problem with equilibrium constraints in finite-dimensional spaces ( $$\text{(NSIMPEC) }$$ for short). For this purpose, we provide some fundamental characterizations for the $$\varPsi $$ -preinvexity involving the notion of contingent epiderivative and contingent hypoderivative of extended-real-valued function and then some sufficient optimality conditions are obtained for the global optimal solution to such problem. For application purpose, a Mond–Weir and Wolfe types dual model for the problem $$\text{(NSIMPEC) }$$ are presented. Especially, some generalized Slater constraint qualifications are proposed and strong/weak duality theorems for the problem $$\text{(NSIMPEC) }$$ and its Mond–Weir and Wolfe types dual model are established. Some illustrative examples also proposed for our findings.

In present study, an interval optimization problem is addressed in which both objective and constraint functions are non-differentiable. The existence of the solution for this problem is investigated. Further, the necessary and sufficient optimality conditions are explored. Moreover, the weak and strong duality relations between the primal and the corresponding dual interval optimization problem are established. Counterexamples are discussed to justify the present work.

Two different pairs of higher-order symmetric dual programs such as Wolfe type and Mond–Weir type are studied. The weak, strong and converse duality theorems are established for the higher-order symmetric dual programs under higher-order $$\rho -(\eta ,\theta )-$$ invexity and $$\rho -(\eta ,\theta )-$$ pseudo-invexity assumptions. Many examples and counterexamples are illustrated to justify our work. We also observe that several known results are obtained as special cases.

In the present paper, we consider Mond-Weir type nondifferentiable second order fractional symmetric dual programs over arbitrary cones and derive duality results under second order K−F-convexity/K−F-pseudoconvexity assumptions. Our results generalize several known results in the literature.

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (θ, η, ρ)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is η-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

In this paper we consider the dual problems for multiobjective programming with generalized convex functions. We obtain the weak duality and the strong duality. At last, we give an equivalent relationship between saddle point and efficient solution in multiobjective programming.