相关论文: Set-optimization meets variational inequalities

In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…

In this paper, we provide some sufficient conditions for the existence of solutions to non-monotone Variational Inequalities (VIs) based on inverse mapping theory and degree theory. We have obtained several applicable sufficient conditions…

We consider the solution of a stochastic convex optimization problem $\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime where $\theta^*$ is unavailable and $\xi$ is a suitably defined random variable. Instead,…

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

In this article, we work with set-valued optimization problems in locally convex topological vector spaces. We prove the equivalencies of some definitions of generalized convex maps introduced by Jeyakumar, Yang, Yang & Yang & Chen, as well…

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

We establish existence results of Hartmann-Stampacchia type for a class of variational-hemivariationalinequalities on closed and convex sets (either bounded or unbounded) in a Hilbert space.

We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward…

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are…

We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponing complete lattice of sets. A function mappping into the preordered set is extended to a…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

This article presents nonlinear conjugate gradient methods for finding local weakly minimal points of set-valued optimization problems under a lower set less ordering relation. The set-valued objective function of the optimization problem…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…

In this paper, we discuss scalar Lagrangian multipliers and vector Lagrangian multipliers for constrained set-valued optimization problems. We obtain some necessary conditions, sufficient conditions, as well as necessary and sufficient…

In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify existing conditions as well as present new conditions that are…

Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive…