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Related papers: Forward-backward-forward dynamics for bilevel equi…

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Backward Filtering Forward Guiding (BFFG) is a bidirectional algorithm proposed in Mider et al. [2021] and studied more in depth in a general setting in Van der Meulen and Schauer [2022]. In category theory, optics have been proposed for…

Category Theory · Mathematics 2026-03-25 Moritz Schauer , Frank van der Meulen , Andi Q. Wang

In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng's…

Optimization and Control · Mathematics 2021-04-28 Yunier Bello-Cruz , Oday Hazaimah

In this paper, we propose and analyze a third-order dynamical system for solving a generalized inverse mixed variational inequality problem in a Hilbert space H. We establish the existence and uniqueness of the trajectories generated by the…

Optimization and Control · Mathematics 2026-02-13 Nam Van Tran

In this article, we aim to approximate a solution to the bilevel equilibrium problem $\mathbf{(BEP})$ for short: find $\bar{x} \in \mathbf{S}_f$ such that $ g(\bar{x}, y) \geq 0, \,\, \forall y \in \mathbf{S}_f, $ where $ \mathbf{S}_f = \{…

Optimization and Control · Mathematics 2025-03-03 Aicha Balhag , Zakaria Mazgouri , Hassan Riahi , Michel Théra

We study acceleration and preconditioning strategies for a class of Douglas-Rachford methods aiming at the solution of convex-concave saddle-point problems associated with Fenchel-Rockafellar duality. While the basic iteration converges…

Optimization and Control · Mathematics 2016-04-22 Kristian Bredies , Hongpeng Sun

This article introduces a novel approach to learning monotone neural networks through a newly defined penalization loss. The proposed method is particularly effective in solving classes of variational problems, specifically monotone…

Optimization and Control · Mathematics 2025-03-07 Younes Belkouchi , Jean-Christophe Pesquet , Audrey Repetti , Hugues Talbot

In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…

Optimization and Control · Mathematics 2023-06-29 Luis M. Briceno-Arias , Francisco José Silva , Xianjin Yang

In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…

Analysis of PDEs · Mathematics 2025-08-19 Dian Feng , Yikan Liu , Shuai Lu

In this paper, we analyze the iteration-complexity of Generalized Forward--Backward (GFB) splitting algorithm, as proposed in \cite{gfb2011}, for minimizing a large class of composite objectives $f + \sum_{i=1}^n h_i$ on a Hilbert space,…

Optimization and Control · Mathematics 2014-02-11 Jingwei Liang , Jalal M. Fadili , Gabriel Peyré

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms and has been applied to many machine learning tasks such as data cleaning, few-shot learning, and neural architecture search. However,…

Machine Learning · Computer Science 2022-05-04 Junyi Li , Feihu Huang , Heng Huang

In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…

Optimization and Control · Mathematics 2020-10-22 Erfan Yazdandoost Hamedani , Necdet Serhat Aybat

In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…

Optimization and Control · Mathematics 2018-04-06 Nguyen The Vinh

We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator $T$ and a single-valued monotone, Lipschitz continuous, and expectation-valued operator $V$. We draw motivation…

Optimization and Control · Mathematics 2022-08-11 Shisheng Cui , Uday V. Shanbhag , Mathias Staudigl , Phan Tu Vuong

In this paper we address planning problems in high-dimensional hybrid configuration spaces, with a particular focus on manipulation planning problems involving many objects. We present the hybrid backward-forward (HBF) planning algorithm…

Robotics · Computer Science 2016-11-18 Caelan Reed Garrett , Tomas Lozano-Perez , Leslie Pack Kaelbling

In this paper an explicit algorithm is proposed for solving an equilibrium problem whose associated bifunction is pseudomonotone and satisfies a Lipschitz-type condition. Contrary to many algorithms, our algorithm is done without using…

Optimization and Control · Mathematics 2019-07-10 Dang Van Hieu , Jean Jacques Strodiot , Le Dung Muu

We propose a variable metric forward-backward splitting algorithm and prove its convergence in real Hilbert spaces. We then use this framework to derive primal-dual splitting algorithms for solving various classes of monotone inclusions in…

Optimization and Control · Mathematics 2012-06-29 Patrick L. Combettes , Bang C. Vũ

In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower…

Optimization and Control · Mathematics 2014-03-26 Boushra Abbas , Hedy Attouch

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of…

Optimization and Control · Mathematics 2014-07-09 G. C. Bento , J. X. Cruz Neto , J. O. Lopes , P. A. Soares , A. Soubeyran

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…

Probability · Mathematics 2026-05-01 Matteo Casserini , Gechun Liang

We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate…

Numerical Analysis · Mathematics 2018-02-21 Olivier Bokanowski , Athena Picarelli , Christoph Reisinger