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We generalize recent results on the monotonicity method, for inclusion detection in the partial data anisotropic Calder\'on problem, to very general non-self-adjoint perturbations. This involves a forward model that accounts for both the…

Analysis of PDEs · Mathematics 2026-05-07 Henrik Garde , David Johansson , Thanasis Zacharopoulos

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

Machine Learning · Computer Science 2023-09-29 Jérôme Bolte , Edouard Pauwels , Antonio Silveti-Falls

Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…

Optimization and Control · Mathematics 2026-02-10 Roger Behling , Yunier Bello-Cruz , Alfredo Iusem , Di Liu , Luiz-Rafael Santos

We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…

Optimization and Control · Mathematics 2016-02-26 Lorenzo Rosasco , Silvia Villa , Bang Cong Vu

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Optimization and Control · Mathematics 2017-06-20 Quang Van Nguyen , Olivier Fercoq , Volkan Cevher

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…

Machine Learning · Computer Science 2026-05-13 Takashi Furuya , Yury Korolev , Takaharu Yaguchi

We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the cocoercivity of some of the operators appearing in the model. Several…

Optimization and Control · Mathematics 2011-10-11 Bang Cong Vu

Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…

Functional Analysis · Mathematics 2025-06-25 Minh N. Bùi , Patrick L. Combettes

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…

Optimization and Control · Mathematics 2025-12-12 Chenglong Bao , Yancheng Yuan , Shulan Zhu

In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…

Optimization and Control · Mathematics 2022-11-01 A. A. Titov , S. S. Ablaev , M. S. Alkousa , F. S. Stonyakin , A. V. Gasnikov

We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…

Optimization and Control · Mathematics 2025-12-16 Felipe Atenas , Farhana Ahmed Simi , Matthew K Tam

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Machine Learning · Statistics 2015-12-31 Ravi Ganti , Laura Balzano , Rebecca Willett

We introduce an inertial quasi-Newton Forward-Backward Splitting Algorithm to solve a class of monotone inclusion problems. While the inertial step is computationally cheap, in general, the bottleneck is the evaluation of the resolvent…

Optimization and Control · Mathematics 2024-03-18 Shida Wang , Jalal Fadili , Peter Ochs

We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the proximal composition, a convexity-preserving operation between a linear operator and a function.…

Optimization and Control · Mathematics 2023-07-25 Patrick L. Combettes

Resolvents of set-valued operators play a central role in various branches of mathematics and in particular in the design and the analysis of splitting algorithms for solving monotone inclusions. We propose a generalization of this notion,…

Optimization and Control · Mathematics 2020-06-24 Minh N. Bùi , Patrick L. Combettes

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

Numerical Analysis · Mathematics 2018-06-05 Robert Plato , Bernd Hofmann

The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed convex sets to a given point in a Hilbert space. In this work, we generalize the scheme so that it…

Optimization and Control · Mathematics 2024-01-03 F. J. Aragón Artacho , R. Campoy

A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…

Optimization and Control · Mathematics 2009-11-13 Patrick L. Combettes , Jean-Christophe Pesquet

We present a new primal-dual splitting algorithm for structured monotone inclusions in Hilbert spaces and analyze its asymptotic behavior. A novelty of our framework, which is motivated by image recovery applications, is to consider…

Optimization and Control · Mathematics 2014-12-15 Stephen Becker , Patrick L. Combettes

We propose a variation of the forward--backward splitting method for solving structured monotone inclusions. Our method integrates past iterates and two deviation vectors into the update equations. These deviation vectors bring flexibility…

Optimization and Control · Mathematics 2023-07-14 Hamed Sadeghi , Sebastian Banert , Pontus Giselsson