Related papers: A note on optimization in $\mathbb{R}^n$
In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.
This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence,…
In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with…
The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator…
We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. Focusing on a stochastic query model that provides noisy evaluations of the operator, we analyze a variance-reduced stochastic…
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 introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…
The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…
Banach's fixed point theorem for contraction maps has been widely used to analyze the convergence of iterative methods in non-convex problems. It is a common experience, however, that iterative maps fail to be globally contracting under the…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in the spaces $\rr^N$, with varying $N$. The error of such…
We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach…
This paper first proves two fixed point theorems in complete random normed modules, which are respectively the random generalizations of the classical Banach's contraction mapping principle and Browder--Kirk's fixed point theorem. As…