Related papers: Variable Metric Quasi-Fej\'er Monotonicity
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…
Self consistent transfer operators arise naturally in the study of mean-field coupled dynamical systems and are closely related to kinetic PDEs such as the Vlasov equation. Despite substantial progress on existence and uniqueness of fixed…
The joint alignment of multivariate functional data plays an important role in various fields such as signal processing, neuroscience and medicine, including the statistical analysis of data from wearable devices. Traditional methods often…
Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
The object of investigation in this paper are vector nonlinear programming problems with cone constraints. We introduce the notion of a Fritz John pseudoinvex cone-constrained vector problem. We prove that a problem with cone constraints is…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a…
We propose an alternative approach to neural network training using the monotone vector field, an idea inspired by the seminal work of Juditsky and Nemirovski [Juditsky & Nemirovsky, 2019] developed originally to solve parameter estimation…
Fej\'er's theorem guarantees norm convergence of Ces\`aro means of Taylor partial sums in the Hardy space, whereas such convergence generally fails in weighted Dirichlet-type spaces, especially in the higher-order setting. In this paper, we…
Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…
The study of first-order optimization algorithms (FOA) typically starts with assumptions on the objective functions, most commonly smoothness and strong convexity. These metrics are used to tune the hyperparameters of FOA. We introduce a…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from,…
A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results…