Related papers: Some enhanced existence results for strong vector …
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a…
In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's…
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…
The paper is devoted to the existence of weak Pareto solutions and the weak sharp minima at infinity property for a general class of constrained nonconvex vector optimization problems with unbounded constraint set via asymptotic cones and…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
We deal with linear programming problems involving absolute values in their formulations, so that they are no more expressible as standard linear programs. The presence of absolute values causes the problems to be nonconvex and nonsmooth,…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…
We study momentum-based first-order optimization algorithms in which the iterations utilize information from the two previous steps and are subject to an additive white noise. This setup uses noise to account for uncertainty in either…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
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…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
In this paper, we introduce a new concept of generalized convexity for E-differentiable vector optimization problems. Namely, the notion of exponentially E-invexity is defined. Further, some properties and results of exponentially E-invex…
The present paper deals with the perturbation analysis of set-valued inclusion problems, a problem format whose relevance has recently emerged in such contexts as robust and vector optimization as well as in vector equilibrium theory. The…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…