Our objective in the present article is to reframe the ideology of the ℰ -LU-Pareto solution for nonsmooth semi-infinite programs with multiple intervals. First of all, using the scalarization method, we establish the relation between the ℰ -LU-Pareto solution and the ℰ -LU-optimal solution. Moreover, we figure out ℰ -necessary and sufficient optimality conditions under the constraint qualification named Farkas-Minkowski using the notion of approximate subdifferentials. Additionally, we construct a dual model with the mixed-type approximation that combines features of both the Mond-Weir and Wolfe-type dual formulations. Subsequently, we derive weak and strong duality results within the context of convexity and generalized convexity. Finally, we show that the projected mixed dual model can be transformed into both the Mond-Weir and Wolfe-type dual models.

In the present work, we construct a second order symmetric dual pair with multiobjective and nondifferentiable settings over variational problems and explore weak, strong, and converse duality theorems with the help of second order (F, alpha, rho, d)-convexity. First, a parametric method is used to transform the problem into an equivalent non-fractional form. In order to determine the bound on the optimal value of the primal problem and build the theoretical framework for strong duality, we then deduce the weak duality theorem for the designed problems. The strong duality demonstrated in the paper shows that a symmetric relationship exists between the primal and dual problems. The static case is additionally addressed by dropping the time component. The solutions in our work may be applied to a broader class of problems that arise in modeling mechanical engineering problems. The existence of the problem as required in the discussion is demonstrated by constructed examples.

In this article, we explore the concept of interval-valued nonsmooth optimization problems using r-invexity in relation to convex compact sets. For the selected nonsmooth interval-valued problem (IP), we derive necessary and sufficient optimality criteria. In addition to that, we establish various duality theorems under r-invex quasidifferentiable with respect to a convex compact set that is equal to the Minkowski sum of their subdifferentials and superdifferentials. We draft a numerical example to support the results obtained in this paper. It is important to note that the Lagrange multipliers are nonconstant for the considered problem.

The present article considers a nonsmooth interval-valued vector optimization problem with inequality constraints. We first figure out Fritz John and Karush-Kuhn-Tucker type necessary optimality conditions for the interval-valued problem designed in the paper under quasidifferentiable -convexity in connection with compact convex sets. Subsequently, sufficient optimality conditions are extrapolated under aforesaid quasidifferentiability supported by a suitable numerical example.

In the present article, we employ the concept of an ℰ -LU-optimal solution to explore the nonsmooth semi-infinite interval-valued programming problems. First of all, we formulate the ℰ -necessary and ℰ -sufficient optimality conditions for the ℰ -LU-optimal solution under appropriate convexity and using approximate subdifferentials. After that, we construct the Mond–Weir and Wolfe-type dual models and propose ℰ -weak and ℰ -strong duality theorems for both the constructed dual models.

In the article, one formulates Fritz John type and Karush-Kuhn-Tucker type necessary conditions for an interval-valued vector equilibrium problem having a locally LU-efficient solution, where convexificators demonstrate the solutions that are regular. Sufficient conditions for a locally weak LU-efficient solution have been entrenched by imposing appropriate assumptions along with generalized convexity. Some applications are presented for a constrained intervalvalued vector variational inequality and a constrained interval-valued vector optimization problem.

Our objective in this article is to explore the idea of an unconstrained problem using the exact l1 penalty function for the nonsmooth multiobjective interval-valued problem (MIVP) having inequality and equality constraints. First of all, we figure out the KKT-type optimality conditions for the problem (MIVP). Next, we establish the equivalence between the set of weak LU-efficient solutions to the problem (MIVP) and the penalized problem (MIVP rho) with the exact l1 penalty function. The utility of this transformation lies in the fact that it converts constrained problems to unconstrained ones. To accurately predict the applicability of the results presented in the paper, meticulously crafted examples are provided.

Our goal in this paper is to retain the ideology of convexificators to construct adequate Fritz John and KKT optimality conditions for nonsmooth programming problems with local weakly LU-Pareto solutions having inequality, equality, and set constraints in Banach space where the involved functions admit convexificators. Sufficiency criteria for local weakly LU-Pareto solutions have been formulated under suitable conditions on the generalized convexity. The desired duality theorems have been proposed for both Mond-Weir dual problems (MDCIMP) and Wolfe-type dual problems (WDCIMP). Numerical examples are constructed to justify the methodology adopted in the paper. Our paper extends some of the recently published articles to a great extent.

The article aims at higher order fractional variational pair of symmetric dual formulations where constraints are defined over cones and explores pertinent duality output applying the idea of higher order ?-invexity. Also, we bring into begin a numerical example in order to validate the definition exploited to establish duality results. Moreover, we demonstrate a case study dealing with the static formulation of our considered problem and explore the results carefully.

The present article explores the way eta-approximated method is applied to substantiate duality results for the fractional variational problems under invexity. eta-approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases.

In this paper, efforts have been taken to generalise the notion of anti-fuzzy subgroup. Proposed definition was supported by graphical comparison with our previous result and suitably constructed examples. Based on the introduced definition, we derive not only some results of anti-fuzzy subgroup but also we redefine lower level set and lower level subgroup, and derive some essential theorems to study some algebraic characteristics. Further, a modified notion of lower level subgroup is given.

The present work frames a pair of symmetric dual problems for second order nondifferentiable fractional variational problems over cone constraints with the help of support functions. Weak, strong and converse duality theorems are derived under second order F-convexity assumptions. By removing time dependency, static case of the problem is obtained. Suitable numerical example is constructed.

In the present paper, we introduce a pair of second order fractional symmetric variational programs over cone constraints and derive weak, strong, and converse duality theorems under second order F-convexity assumptions. Moreover, self duality theorem is also discussed. Our results give natural unification and extension of some previously known results in the literature.

In this paper, we have taken step in the direction to establish weak, strong and strict converse duality theorems for three types of dual models related to multiojective fractional programming problems involving ($H_p$, r)-invex functions.

Abstract In the present paper, we examine duality results for Wolfe-type second-order fractional symmetric dual programs. These duality results are then used to investigate minimax mixed integer symmetric dual fractional programs. We also discuss self-duality results at the end.

In the present paper, we move forward in the study of minimax fractional programming problem and establish sufficient optimality conditions under the assumptions of generalized (H-p, r)-invexity. Weak, strong and strict converse duality theorems are also derived for two types of dual models related to minimax fractional programming problem involving aforesaid invex functions. In order to show the existence of introduced class of functions, examples are given.

In this paper, we start our discussion with a pair of multiobjective Mond- Weir type second-order symmetric dual fractional programming problem and derive weak, strong and strict duality theorems under second-order (ϕ, ρ)-invexity assumptions.

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.

In this paper, a pair of Mond-Weir type higher order fractional symmetric dual program over cone constraints is formulated. Under higher order invexity assumptions, we prove weak, strong and strict duality theorems. Moreover, a self dual program is formulated and self duality theorem is discussed.

The present paper is framed to study weak, strong and strict converse duality relations for a semi-infinite programming problem and its Wolfe and Mond-Weir-type dual programs under generalized (Hp,r)Open image in new window-invexity.