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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

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…

Optimization and Control · Mathematics 2022-05-23 Xin He , Rong Hu , Ya-Ping Fang

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

Optimization and Control · Mathematics 2022-02-10 Yujia Jin , Aaron Sidford , Kevin Tian

This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs).…

Numerical Analysis · Mathematics 2023-12-20 Long Chen , Ruchi Guo , Jingrong Wei

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

Optimization and Control · Mathematics 2017-08-01 Anastasia Bayandina , Alexander Gasnikov , Evgenia Gasnikova , Sergey Matsievsky

We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…

Optimization and Control · Mathematics 2019-04-01 Fatemeh Mansoori , Ermin Wei

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Optimization and Control · Mathematics 2017-11-21 Radu Ioan Bot , Ernö Robert Csetnek , Dennis Meier

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

We propose a new primal-dual homotopy smoothing algorithm for a linearly constrained convex program, where neither the primal nor the dual function has to be smooth or strongly convex. The best known iteration complexity solving such a…

Optimization and Control · Mathematics 2018-10-25 Xiaohan Wei , Hao Yu , Qing Ling , Michael J. Neely

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…

Optimization and Control · Mathematics 2016-05-11 Alexey Chernov , Pavel Dvurechensky , Alexander Gasnikov

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

Optimization and Control · Mathematics 2024-01-17 Xiaokai Chang , Junfeng Yang , Hongchao Zhang

We investigate the integration of Nesterov-type acceleration into primal-dual methods for structured convex optimization. While proximal splitting algorithms efficiently handle composite problems of the form $\min_x f(x)+g(x)+h(Kx)$,…

Optimization and Control · Mathematics 2026-04-13 Laurent Condat , Abdurakhmon Sadiev , Peter Richtárik

In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator which is split as a sum of three operators: the first is continuous single-valued, the second is…

Optimization and Control · Mathematics 2025-03-04 Flavia Chorobura , Ion Necoara , Jean-Christophe Pesquet

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

Systems and Control · Computer Science 2018-04-25 Ivano Notarnicola , Giuseppe Notarstefano

We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…

Optimization and Control · Mathematics 2016-07-27 Brendan O'Donoghue , Eric Chu , Neal Parikh , Stephen Boyd

In this paper we consider a class of monotone inclusion (MI) problems of finding a zero of the sum of two monotone operators, in which one operator is maximal monotone while the other is {\it locally Lipschitz} continuous. We propose…

Optimization and Control · Mathematics 2024-09-04 Zhaosong Lu , Sanyou Mei

In this paper, we study inclusion problems where the involved operators may not be monotone in the classical sense. Specifically, we assume the operators to be generalized monotone, a weaker notion than classical monotonicity. This allows…

Optimization and Control · Mathematics 2025-03-12 Nam Van Tran

Based on the idea of randomized coordinate descent of $\alpha$-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a…

Optimization and Control · Mathematics 2015-10-01 Pascal Bianchi , Walid Hachem , Franck Iutzeler

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

Optimization and Control · Mathematics 2017-09-18 Andrea Simonetto , Hadi Jamali-Rad

Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…

Numerical Analysis · Mathematics 2020-02-25 Erdem Altuntac