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We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…

Optimization and Control · Mathematics 2013-03-13 Radu Ioan Bot , Ernö Robert Csetnek , Andre Heinrich

This paper considers the relaxed Peaceman-Rachford (PR) splitting method for finding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general…

Optimization and Control · Mathematics 2017-11-07 Renato D. C. Monteiro , Chee-Khian Sim

In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…

Optimization and Control · Mathematics 2016-04-05 Mingyi Hong

This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional…

Machine Learning · Computer Science 2025-09-29 Yingying Li , Mingxuan Xie , Hailong You , Yongqiang Yao , Hongwei Liu

This paper introduces a unified framework for accelerated gradient methods through the variable and operator splitting (VOS). The operator splitting decouples the optimization process into simpler subproblems, and more importantly, the…

Optimization and Control · Mathematics 2025-05-08 Long Chen , Luo Hao , Jingrong Wei

This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…

Optimization and Control · Mathematics 2023-01-05 Weiwei Kong , Renato D. C. Monteiro

Moving Horizon Estimation~(MHE) is essentially an optimization-based approach designed to estimate the states of dynamic systems within a moving time horizon. Traditional MHE solutions become computationally prohibitive due to the…

Systems and Control · Electrical Eng. & Systems 2025-08-22 Shuting Wu , Yifei Wang , Jingzhe Wang , Apostolos I. Rikos , Xu Du

This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex functions: the first function is smooth with up to the d-th…

Optimization and Control · Mathematics 2020-04-20 Bo Jiang , Haoyue Wang , Shuzhong Zhang

In this paper we provide a generalization of the Douglas-Rachford splitting (DRS) and the primal-dual algorithm (Vu 2013, Condat 2013) for solving monotone inclusions in a real Hilbert space involving a general linear operator. The proposed…

Optimization and Control · Mathematics 2021-09-22 Luis M. Briceño-Arias , Fernando Roldán

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

Optimization and Control · Mathematics 2025-11-03 Xian-Jun Long , Kang Zeng , Gao-Xi Li , Minh N. Dao , Zai-Yun Peng

Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…

Optimization and Control · Mathematics 2020-04-01 Andreas Themelis , Panagiotis Patrinos

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

Optimization and Control · Mathematics 2026-05-11 Lixin Tang , Xingyu Wang , Liwei Zhang

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Dynamical Systems · Mathematics 2017-07-07 Zoran Tomljanović , Christopher Beattie , Serkan Gugercin

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

Optimization and Control · Mathematics 2021-04-20 Yuzixuan Zhu , Deyi Liu , Quoc Tran-Dinh

Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…

Optimization and Control · Mathematics 2024-11-12 Ruichen Jiang , Michał Dereziński , Aryan Mokhtari

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 propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…

Machine Learning · Statistics 2019-01-30 Hongzhou Lin , Julien Mairal , Zaid Harchaoui

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

Optimization and Control · Mathematics 2026-03-25 Geng-Hua Li , Hai-Yi Zhao , Xiangkai Sun

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…

Optimization and Control · Mathematics 2018-12-14 Quoc Tran-Dinh , Liang Ling , Kim-Chuan Toh

The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…

Numerical Analysis · Mathematics 2024-07-03 C. Carstensen , N. T. Tran