Multiobjective Semi-infinite Programming Research Articles

Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds

Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds

Lagrange Duality and Saddle Point Optimality Conditions for Multiobjective Semi-Infinite Programming with Vanishing Constraints

The objective of this paper is to investigate multiobjective semi-infinite programming problems with vanishing constraints (in brief, MSIPVC). We firstly propose both the vector Lagrange dual problems and the scalarized Lagrange dual problems for MSIPVC and explore duality relations under convexity assumptions. Then, the saddle point optimality conditions for MSIPVC are considered. Some examples are also given to illuminate the main results.

Optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints on Hadamard manifolds

This article is concerned with nonsmooth multiobjective semi-infinite programming problems with vanishing constraints in the setting of Hadamard manifolds (abbreviated as, (NMSIPVC)). We present the Abadie constraint qualification (abbreviated as, (ACQ)) and a modified version of (ACQ), namely, (NMSIPVC)-tailored Abadie constraint qualification (abbreviated as, (NMSIPVC-ACQ)), for (NMSIPVC). The Karush-Kuhn-Tucker (abbreviated as, KKT) type necessary criteria of optimality for (NMSIPVC) are derived by employing (ACQ) and (NMSIPVC-ACQ). Moreover, sufficient criteria of optimality for (NMSIPVC) are derived under generalized geodesic convexity hypotheses and certain mild restrictions on the index sets. Further, we formulate Wolfe type and Mond-Weir type dual models related to (NMSIPVC) and derive several duality results that relate (NMSIPVC) and the corresponding dual models. Non-trivial numerical examples are incorporated to demonstrate the validity of the results established in this paper. To the best of our knowledge, this is for the first time that constraint qualifications, optimality conditions, and duality results have been investigated for (NMSIPVC) in the setting of Hadamard manifolds.

Second-Order Optimality Conditions and Duality for Multiobjective Semi-Infinite Programming Problems on Hadamard Manifolds

This paper is devoted to the study of multiobjective semi-infinite programming problems on Hadamard manifolds. We consider a class of multiobjective semi-infinite programming problems (abbreviated as MSIP) on Hadamard manifolds. We use the concepts of second-order Karush–Kuhn–Tucker stationary point and second-order Karush–Kuhn–Tucker geodesic pseudoconvexity of the considered problem to derive necessary and sufficient second-order conditions of efficiency, weak efficiency and proper efficiency for MSIP along with certain generalized geodesic convexity assumptions. Moreover, we formulate the second-order Mond–Weir-type dual problem related to MSIP and deduce weak and strong duality theorems relating MSIP and the dual problem. The significance of our results is demonstrated with the help of non-trivial examples. To the best of our knowledge, this is the first time that second-order optimality conditions for MSIP have been studied in Hadamard manifold setting.

Optimality Conditions and Duality for Nonsmooth Multiobjective Semi-infinite Programming Problems on Hadamard Manifolds

Optimality Conditions and Duality for Nonsmooth Multiobjective Semi-infinite Programming Problems on Hadamard Manifolds

Nonsmooth semi-infinite roughly B-invex multi-objective programming problems

In this paper, we will study a nonsmooth semi-infinite multi-objective programming problem involving roughly B-invex functions. Sufficient optimality conditions for the primal problem are derived. We shall formulate Mond–Weir type dual and establish weak and strong duality theorems under various roughly B-invexity assumptions.

On nonsmooth multiobjective semi-infinite programming with switching constraints using tangential subdifferentials

We investigate optimality conditions for a nonsmooth multiobjective semi-infinite programming problem subject to switching constraints. In particular, we employ a surrogate problem and a suitable constraint qualification to state necessary M-stationary conditions in terms of tangential subdifferentials. An example is given at the end to illustrate our main result.

On nondifferentiable semi-infinite multiobjective programming with interval-valued functions

In the paper, we investigate a class of nondifferentiable semi-infinite multiobjective programming problems such that all functions constituting them are interval-valued. We derive both Fritz John necessary optimality conditions and, under a constraint qualification, Karush-Kuhn-Tucker necessary optimality conditions for (weak) $ LU $-Pareto solutions in the considered nondifferentiable semi-infinite vector interval-valued optimization problem. Under appropriate invexity hypotheses, we also prove sufficient optimality conditions for this semi-infinite interval-valued vector optimization problem. Further, we also use the $ l_{1} $ exact function method for solving the aforesaid nondifferentiable interval-valued multicriteria optimization problem. Then, we analyze the property of exactness of the penalization for the absolute value exact penalty function method under assumption that the functions involved in the considered semi-infinite multiobjective programming problem are locally Lipschitz interval-valued invex functions. The conditions guaranteeing the equivalence of the sets of (weak) $ LU $-Pareto solutions in the original semi-infinite interval-valued multiobjective programming problem and its associated vector penalized optimization problem with the multiple interval-valued $ l_{1} $ exact penalty function are given.

On nonsmooth multiobjective semi-infinite programming with switching constraints

On nonsmooth multiobjective semi-infinite programming with switching constraints

Approximate optimality conditions and mixed type duality for semi-infinite multiobjective programming problems involving tangential subdifferentials

The aim of this paper is to study the approximate solution for semi-infinite multiobjective programming problems related to tangential subdifferentials. Under some mild assumptions, we obtain approximate necessary and sufficient optimality conditions of a (weakly) quasi $ \varepsilon $-efficient solution for semi-infinite multiobjective programming problems. We also introduce a mixed type dual model to the semi-infinite multiobjective programming problem, which is different from the one considered in the literature. Finally, we derive some approximate weak, strong and converse duality theorems under the assumptions of generalized convexity. Our results extend and improve the corresponding results in the literature. Some examples are given to illustrate some advantages of our results.

Optimality conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds using generalized geodesic convexity

This paper deals with multiobjective semi-infinite programming problems on Hadamard manifolds. We establish the sufficient optimality criteria of the considered problem under generalized geodesic convexity assumptions. Moreover, we formulate the Mond-Weir and Wolfe type dual problems and derive the weak, strong and strict converse duality theorems relating the primal and dual problems under generalized geodesic convexity assumptions. Suitable examples have also been given to illustrate the significance of these results. The results presented in this paper extend and generalize the corresponding results in the literature.

Robust optimality conditions and duality for nonsmooth multiobjective fractional semi-infinite programming problems with uncertain data

In this article, some Karush-Kuhn-Tucker type robust optimality conditions and duality for an uncertain nonsmooth multiobjective fractional semi-infinite programming problem ((UMFP), for short) are established. First, we provide, by combining robust optimization and the robust limiting constraint qualification, robust necessary optimality conditions in terms of Mordukhovich's subdifferentials. Under suitable assumptions on the generalized convexity/the strictly generalized convexity, robust necessary optimality condition becomes robust sufficient optimality condition. Second, we formulate types of Mond-Weir and Wolfe robust dual problem for (UMFP) via the Mordukhovich subdifferentials. Finally, as an application, we establish weak/strong/converse robust duality theorems for the problem (UMFP) and its Mond-Weir and Wolfe types dual problem. Some illustrative examples are also provided for our findings.

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

Karush-Kuhn-Tucker optimality conditions and duality for nonsmooth multiobjective semi-infinite programming problems with vanishing constraints

Corrigendum on: Optimality conditions and duality for multiobjective semi-infinite programming with data uncertainty via Mordukhovich subdifferential (Yugoslav Journal of Operations Research, vol. 31, no 4, doi: https://doi.org/10.2298/YJOR201017013P)

The author of the article "Optimality Conditions and Duality for Multiobjective Semi-Infinite Programming with Data Uncertainity via Mordukhovich Subdifferential", Thanh-Hung Pham has informed the Editor about necessary corrections of the paper. <br><br><font color="red"><b> Link to the corrected article <u><a href="http://dx.doi.org/10.2298/YJOR201017013P">10.2298/YJOR201017013P</a></b></u>

Necessary optimality conditions for a multiobjective semi-infinite interval-valued programming problem

Necessary optimality conditions for a multiobjective semi-infinite interval-valued programming problem

Optimality Conditions and Duality for Multiobjective Semi-infinite Programming on Hadamard Manifolds

Optimality Conditions and Duality for Multiobjective Semi-infinite Programming on Hadamard Manifolds

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality conditions and, under appropriate invexity hypotheses, sufficient optimality conditions are proved for such nonconvex smooth vector optimization problems. Further, vector duals in the sense of Mond–Weir are defined for the considered differentiable semi-infinite multiobjective programming problems with vanishing constraints and several duality results are established also under invexity hypotheses.

Comments on “Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming”

Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vec- tor programming problem are given in the paper by Jennane et al. (RAIRO:OR (2020). DOI: 10.1051/ro/2020066). Having noticed inconsistencies in their paper, Gadhi and Ichatouhane (RAIRO:OR (2020). DOI: 10.1051/ro/2020107) made the necessary corrections and proposed what they considered a more pertinent formulation of their main Theorem. Recently, Jennane et al. (RAIRO:OR (2020). DOI: 10.1051/ro/2020134) have criticised our work. This note is a critical response to this criticism.

Erratum to “Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming”

This note corrects an error in our paper [RAIRO: OR 55 (2021) 1–11] as we should drop the expression “with at least one strict inequality” in the definition of interval order in Section 2. Instead of proposing this short amendment, the authors of [RAIRO: OR 55 (2021) 13–22] gave a proposition that requires an additional condition on the constraint functions. However, we claim that all the results of our paper are correct once the modification above is done.

Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming

We consider a nonsmooth semi-infinite interval-valued vector programming problem, where the objectives and constraint functions need not to be locally Lipschitz. Using Abadie’s constraint qualification and convexificators, we provide Karush–Kuhn–Tucker necessary optimality conditions by converting the initial problem into a bi-criteria optimization problem. Furthermore, we establish sufficient optimality conditions under the asymptotic convexity assumption.