Related papers: Constrained Ordered Equilibrium Problems
We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential…
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
This paper addresses the challenge of proving the existence of solutions for nonlinear equations in Banach spaces, focusing on the Navier-Stokes equations and discretizations of thom. Traditional methods, such as monotonicity-based…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly convex-strongly concave objective functions, we establish…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
This paper studies the saddle point problem of polynomials. We give an algorithm for computing saddle points. It is based on solving Lasserre's hierarchy of semidefinite relaxations. Under some genericity assumptions on defining…
In this article we extend the notion of orthogonal metric space to weak orthogonal metric space. Then we establish fixed point results for a mapping satisfying a more general contraction condition. Several nontrivial examples are given in…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
We establish some new common fixed point theorems of single-valued and multivalued mappings operating between complete ordered locally convex spaces under weaker assumptions. As an application, we prove a new minimax theorem of existence of…
We study a class of quasi-variational inequality problems defined over infinite dimensional Banach space and deduce sufficient conditions for ensuring solutions to such problems under the upper semi-continuity and pseudomonotonicity…
In this paper, we will define generalized critical point, ordered extreme and order monotone property of single-valued mappings in partially ordered Banach spaces. In particular, we will find the explicit formulas of Gateaux and Frechet…
In this paper, we study the existence of the random fixed points for lower semicontinuous condensing random operators defined on Banach spaces. Our results extend corresponding ones present in literature.
This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…
In the present article, we show the existence of a coupled fixed point for an order preserving mapping in a preordered left K-complete quasi-pseudometric space using a preorder induced by an appropriate function. We also define the concept…