Related papers: Optimality conditions and duality relations in non…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
This paper deals with approximate Pareto solutions of a nonsmooth interval-valued multiobjective optimization problem with data uncertainty in constraints. We first introduce some kinds of approximate Pareto solutions for the robust…
We employ a fuzzy optimality condition for the Frechet subdifferential and some advanced techniques of variational analysis such as formulae for the subdifferentials of an infinite family of nonsmooth functions and the coderivative…
This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…
One of the most important optimality conditions to aid to solve a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality…
In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…
This paper is devoted to the study of approximate solutions for a multiobjective interval-valued optimization problem based on an interval order. We establish new existence theorems of approximate solutions for such a problem under some…
In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust…
The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
These lecture notes for a graduate course cover generalized derivative concepts useful in deriving necessary optimality conditions and numerical algorithms for nondifferentiable optimization problems in inverse problems, imaging, and…
In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order…
Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function $\tilde{f}$, new necessary and sufficient optimality conditions are…
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
The KKT optimality conditions for multi-objective interval-valued optimization problem on Hadamard manifold are studied in this paper. Several concepts of Pareto optimal solutions, considered under LU and CW ordering on the class of all…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential…