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We consider primal-dual mixed finite element methods for the solution of the elliptic Cauchy problem, or other related data assimilation problems. The method has a local conservation property. We derive a priori error estimates using known…

Numerical Analysis · Mathematics 2018-01-01 Erik Burman , Mats. G. Larson , Lauri Oksanen

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…

Computer Vision and Pattern Recognition · Computer Science 2023-09-08 Gabriel Moreira , Manuel Marques , João Paulo Costeira

This paper presents a multilevel FISTA algorithm, based on the use of the Moreau envelope to build the correction brought by the coarse models, which is easy to compute when the explicit form of the proximal operator of the considered…

Optimization and Control · Mathematics 2022-10-31 Guillaume Lauga , Elisa Riccietti , Nelly Pustelnik , Paulo Gonçalves

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…

Optimization and Control · Mathematics 2014-10-28 Jean-Christophe Pesquet , Audrey Repetti

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the…

Optimization and Control · Mathematics 2023-07-25 Le Thi Khanh Hien , Renbo Zhao , William B. Haskell

This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…

Optimization and Control · Mathematics 2024-08-28 Wenqiang Pu , Kaizhao Sun , Jiawei Zhang

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

Optimization and Control · Mathematics 2025-07-10 Ronak Mehta , Jelena Diakonikolas , Zaid Harchaoui

This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the…

Optimization and Control · Mathematics 2025-08-12 Adilet Otemissov , Alina Abdikarimova

We study the ridge regression (L2 regularized least squares) problem and its dual, which is also a ridge regression problem. We observe that the optimality conditions describing the primal and dual optimal solutions can be formulated in…

Numerical Analysis · Mathematics 2018-01-22 Ademir Alves Riberio , Peter Richtárik

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

Optimization and Control · Mathematics 2017-10-09 Junyu Zhang , Shiqian Ma , Shuzhong Zhang

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…

Optimization and Control · Mathematics 2024-10-04 Ignace Loris , Simone Rebegoldi

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

Numerical Analysis · Mathematics 2025-08-05 Tatiana A. Bubba , Tommi Heikkilä , Demetrio Labate , Luca Ratti

We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…

Optimization and Control · Mathematics 2022-02-23 Erfan Yazdandoost Hamedani , Necdet Serhat Aybat

We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…

Numerical Analysis · Mathematics 2022-11-02 Stephan Hilb , Andreas Langer

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…

Optimization and Control · Mathematics 2017-09-27 Aurélien Ouattara , Anil Aswani

We study the problem of minimizing the average of a large number of smooth convex functions penalized with a strongly convex regularizer. We propose and analyze a novel primal-dual method (Quartz) which at every iteration samples and…

Optimization and Control · Mathematics 2014-11-24 Zheng Qu , Peter Richtárik , Tong Zhang

Primal-dual algorithm (PDA) is a classic and popular scheme for convex-concave saddle point problems. It is universally acknowledged that the proximal terms in the subproblems about the primal and dual variables are crucial to the…

Optimization and Control · Mathematics 2025-04-24 Shuning Liu , Zexian Liu

Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…

Optimization and Control · Mathematics 2026-02-12 Mateo Díaz , Pedro Izquierdo Lehmann , Haihao Lu , Jinwen Yang

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total…

Optimization and Control · Mathematics 2014-10-27 Vittorio Latorre