Related papers: A note on optimization in $\mathbb{R}^n$
We augment the dimension of the Euclidean space by one and the Picard iteration of a contraction by a simple iteration on the real line such that the resulting iteration becomes monotone increasing and bounded with respect to the order…
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
The aim of this paper is to establish strong convergence theorems for a strongly relatively nonexpansive sequence in a smooth and uniformly convex Banach space. Then we employ our results to approximate solutions of the zero point problem…
The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a…
In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…
In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.
In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…
This paper establishes the existence and uniqueness of solutions for rough differential equations driven by reduced rough paths with low regularity, specifically in the roughness regime $\frac{1}{3} < \alpha \leq \frac{1}{2}$. While the…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
We consider a chemical reaction network governed by mass action kinetics and composed of N different species which can reversibly form heterodimers. A fast iterative algorithm is introduced to compute the equilibrium concentrations of such…
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…
In this paper, we study some optimization problems in uniformly convex and uniformly smooth Bochner spaces. We consider four cases of the underlying subsets: closed and convex subsets, closed and convex cones, closed subspaces and closed…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…