Related papers: An inertial proximal splitting algorithm for hiera…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We prove that…
Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…
Obtaining high-precision guaranteed lower eigenvalue bounds remains difficult, even though the standard high-order conforming finite element (FEM) easily yields extremely sharp upper bounds. Recently developed rigorous approaches using such…
In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…
We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…
The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates $(x_n)$ given by $x_{n+1} = (I+\lambda_n A(\xi_{n+1},\,.\,))^{-1}(x_n)$ where $(A(s,\,.\,):s\in E)$ is a collection of maximal…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based…
This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
The aim of this paper is to study the weak convergence analysis of sequence of iterates generated by a three-operator splitting method of Davis and Yin incorporated with two-step inertial extrapolation for solving monotone inclusion problem…
In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…