-
Article
Optimality Conditions for Nondifferentiable Minimax Programs and Vector Optimization Problems
First-order sufficient optimality conditions in terms of Lagrangian functions and Lagrange multipliers for nondifferentiable minimax programs and vector optimization problems in an Asplund space setting are ob...
-
Article
On Types of Isolated KKT Points in Polynomial Optimization
Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in ℝn. In this paper, the authors are interested in the problem of identifying the type (local minimizer, maximizer o...
-
Article
Minimax programming as a tool for studying robust multi-objective optimization problems
This paper aims to investigate optimality conditions for a weakly Pareto solution to a robust multi-objective optimization problem with locally Lipschitzian data. We do this by using a minimax programming approac...
-
Article
Two Optimal Value Functions in Parametric Conic Linear Programming
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the inequality constraint and the vector defining the objective fun...
-
Article
A dual scheme for solving linear countable semi-infinite fractional programming problems
Using a dual method for solving linear fractional programming problems, we propose an approach to find optimal solutions of linear countable semi-infinite fractional programming problems via optimizing sequenc...
-
Article
Existence of efficient and properly efficient solutions to problems of constrained vector optimization
The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness assumptions on constraint set. The main attent...
-
Article
Quasi \(\epsilon \) -solutions in a semi-infinite programming problem with locally Lipschitz data
Under the fulfilment of the limiting constraint qualification, a necessary condition for a quasi \(\epsilon \) ...
-
Article
On perturbed hybrid steepest descent method with minimization or superiorization for subdifferentiable functions
For finding the minimum value of differentiable functions over a nonempty closed convex subset of a Hilbert space, the hybrid steepest descent method (HSDM) can be applied. In this work, we study perturbed alg...
-
Article
On the existence of Pareto solutions for polynomial vector optimization problems
We are interested in the existence of Pareto solutions to the vector optimization problem $$\begin{aligned} \mathrm{Min}_{\,{\mathbb {R}}^m_+} \{f(x) \,|\, x\in {\mathbb {R}}^n\}, \end{aligned}$$MinR+m{f(x)|x∈Rn}
-
Article
Optimality conditions in convex optimization with locally Lipschitz constraints
In this paper, we consider a convex optimization problem with locally Lipschitz inequality constraints. The KKT optimality conditions (both necessary and sufficient) for quasi
-
Article
On approximate solutions of nondifferentiable vector optimization problems with cone-convex objectives
In this paper, we study a nondifferentiable constrained vector optimization problem where the partial order in the image space is induced by a closed, convex and pointed cone with nonempty interior. Under the C-c...
-
Article
New Second-Order Karush–Kuhn–Tucker Optimality Conditions for Vector Optimization
In the present paper, we focus on the vector optimization problems with constraints, where objective functions and constrained functions are Fréchet differentiable, and whose gradient map** is locally Lipsch...
-
Article
Open AccessExtragradient subgradient methods for solving bilevel equilibrium problems
In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lip...
-
Article
Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications
We establish verifiable conditions for the feasible set of a nonsmooth semi-infinite multiobjective optimization problem to have the normal regularity (that is, the coincidence of the Fréchet normal cone and t...
-
Article
Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces
In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59, 301–323 2012) to multiple set split equilibrium problem (MSSEP) and propose two new p...
-
Article
Existence Theorems in Vector Optimization with Generalized Order
In the present paper, we establish some results for the existence of optimal solutions in vector optimization in infinite-dimensional spaces, where the optimality notion is understood in the sense of generaliz...
-
Article
Nondifferentiable minimax programming problems with applications
This paper is devoted to the study of optimality conditions and duality in nondifferentiable minimax programming problems and applications. Employing some advanced tools of variational analysis and generalized...
-
Article
Extragradient algorithms for equilibrium problems and symmetric generalized hybrid map**s
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid map** in a real H...
-
Article
Qualitative properties of strongly pseudomonotone variational inequalities
Qualitative properties of strongly pseudomonotone variational inequalities such as solution existence, stability and global error bound are studied in this paper.
-
Article
A class of nonsmooth fractional multiobjective optimization problems
This paper focuses on the study of optimality conditions and duality in nonsmooth fractional multiobjective optimization problems. Applying some advanced tools of variational analysis and generalized different...
