Related papers: Minimax-optimal Halpern iterations for Lipschitz m…
In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by…
Under investigation is the problem of finding the best approximation of a function in a Hilbert space subject to convex constraints and prescribed nonlinear transformations. We show that in many instances these prescriptions can be…
We introduce and investigate an iterative scheme for approximating common fixed point of a family of Bregman relatively-nonexpansive mappings in real reflexive Banach spaces. We prove strong convergence theorem of the sequence generated by…
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 investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable…
In this paper, we consider a new iteration process which is faster than all of Picard, Mann, Ishikawa and Agarwal et al. processes. We also prove some strong and weak convergence theorems for the class of nonexpansive mappings in Banach…
This paper is concerned with the sensitivity analysis of a class of parameterized fixed-point problems that arise in the context of obstacle-type quasi-variational inequalities. We prove that, if the operators in the considered fixed-point…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
We propose ECPv2, a scalable and theoretically grounded algorithm for global optimization of Lipschitz-continuous functions with unknown Lipschitz constants. Building on the Every Call is Precious (ECP) framework, which ensures that each…
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…
Fixed point algorithms play an important role to compute feasible solutions to the radio power control problems in wireless networks. Although these algorithms are shown to converge to the fixed points that give feasible problem solutions,…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…
We study the limiting behavior of minimizing $p$-harmonic maps from a bounded Lipschitz domain $\Omega \subset \mathbb{R}^{3}$ to a compact connected Riemannian manifold without boundary and with finite fundamental group as $p \nearrow 2$.…