New efficiency conditions for multiobjective interval-valued programming problems (original) (raw)
Related papers
2015
We devote this paper to study of multiobjective programming problems with interval valued objective functions. For this, we consider two order relations LU and LS on the set of all closed intervals and propose several concepts of Pareto optimal solutions and generalized convexity. Based on generalized convexity (viz. LU and LS-pseudoconvexity) and generalized differentiability (viz. gHdifferentiablity) of interval valued functions, the KKT optimality conditions for aforesaid problems are obtained. The theoretical development is illustrated by suitable examples.
On sufficiency and duality for a class of interval-valued programming problems
Applied Mathematics and Computation
In this paper, we are concerned with an interval-valued programming problem. Sufficient optimality conditions are established under generalized convex functions for a feasible solution to be an efficient solution. Appropriate duality theorems for Mond–Weir and Wolfe type duals are discussed in order to relate the efficient solutions of primal and dual programs.
Necessary optimality conditions of KKT type for interval programming problems
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 2021
This work is concerned with mathematical programming problems with inequality constraints in which the objective function is interval-valued. Necessary optimality conditions of Karush-Kuhn-Tucker type are derived through a geometric approach and the use of the generalized Hukuhara differentiability concept.
Optimality conditions and duality results for non-differentiable interval optimization problems
Journal of Applied Mathematics and Computing, 2015
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.
Optimality conditions and duality for interval-valued optimization problems using convexifactors
Rendiconti del Circolo Matematico di Palermo (1952 -), 2015
This paper is devoted to the applications of convexifactors on interval-valued programming problem. Based on the concept of LU optimal solution, sufficient optimality conditions are established under generalized ∂ *-convexity assumptions. Furthermore, appropriate duality theorems are derived for two types of dual problem, namely Mond-Weir and Wolfe type duals. We also construct examples to manifest the established relations.
Filomat, 2016
In this paper, some interval valued programming problems are discussed. The solution concepts are adopted from Wu [7] and Chalco-Cano et al. [34]. By considering generalized Hukuhara differentiability and generalized convexity (viz. ?-preinvexity, ?-invexity etc.) of interval valued functions, the KKT optimality conditions for obtaining (LS and LU) optimal solutions are elicited by introducing Lagrangian multipliers. Our results generalize the results of Wu [7], Zhang et al. [11] and Chalco-Cano et al. [34]. To illustrate our theorems suitable examples are also provided
The best, the worst and the semi-strong: optimal values in interval linear programming
Croatian Operational Research Review, 2019
Interval programming provides one of the modern approaches to modeling optimization problems under uncertainty. Traditionally, the best and the worst optimal values determining the optimal value range are considered as the main solution concept for interval programs. In this paper, we present the concept of semi-strong values as a generalization of the best and the worst optimal values. Semi-strong values extend the recently introduced notion of semi-strong optimal solutions, allowing the model to cover a wider range of applications. We propose conditions for testing values that are strong with respect to the objective vector, right-hand-side vector or the constraint matrix for interval linear programs in the general form.
A saddle point characterization of efficient solutions for interval optimization problems
Journal of Applied Mathematics and Computing, 2017
In this article, we attempt to characterize efficient solutions of constrained interval optimization problems. Towards this aim, at first, we study a scalarization characterization to capture efficient solutions. Then, with the help of saddle point of a newly introduced Lagrangian function, we investigate efficient solutions of an interval optimization problem. Several parts of the results are supported with numerical and pictorial illustration.
RAIRO Oper. Res., 2021
A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et al. (RAIRO:OR 55 (2021) 1–11.). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to call into question some results on which the main result (Jennane et al. [6] Thm. 4.5) is based. For the convenience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5, and give also a short proof.
On interval-valued optimization problems with generalized invex functions
Journal of Inequalities and Applications, 2013
This paper is devoted to study interval-valued optimization problems. Sufficient optimality conditions are established for LU optimal solution concept under generalized (p, r) -ρ -(η, θ )-invexity. Weak, strong and strict converse duality theorems for Wolfe and Mond-Weir type duals are derived in order to relate the LU optimal solutions of primal and dual problems. MSC: 90C46; 90C26; 90C30