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Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…

Optimization and Control · Mathematics 2025-05-15 Xi Gao , Jinxin Xiong , Linxin Yang , Akang Wang , Weiwei Xu , Jiang Xue

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…

Machine Learning · Computer Science 2013-08-19 Leon Wenliang Zhong , James T. Kwok

An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…

Optimization and Control · Mathematics 2020-10-27 Jianchao Bai , William W. Hager , Hongchao Zhang

This paper is devoted to the design of an efficient and convergent {semi-proximal} alternating direction method of multipliers (ADMM) for finding a solution of low to medium accuracy to convex quadratic conic programming and related…

Optimization and Control · Mathematics 2014-09-10 Xudong Li , Defeng Sun , Kim-Chuan Toh

This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…

Optimization and Control · Mathematics 2020-06-09 Liang Chen , Defeng Sun , Kim-Chuan Toh , Ning Zhang

We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then…

Optimization and Control · Mathematics 2017-06-21 Alnur Ali , Eric Wong , J. Zico Kolter

In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it…

Optimization and Control · Mathematics 2018-08-31 Amir Ali Ahmadi , Anirudha Majumdar

Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory…

Optimization and Control · Mathematics 2023-11-27 Federico Battista , Marianna De Santis

Alternating direction methods of multipliers (ADMMs) are popular approaches to handle large scale semidefinite programs that gained attention during the past decade. In this paper, we focus on solving doubly nonnegative programs (DNN),…

Optimization and Control · Mathematics 2020-09-15 Martina Cerulli , Marianna De Santis , Elisabeth Gaar , Angelika Wiegele

Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting…

Optimization and Control · Mathematics 2021-12-28 Nikitas Rontsis , Paul J. Goulart , Yuji Nakatsukasa

We investigate the local linear convergence properties of the Alternating Direction Method of Multipliers (ADMM) when applied to Semidefinite Programming (SDP). A longstanding belief suggests that ADMM is only capable of solving SDPs to…

Optimization and Control · Mathematics 2026-05-19 Shucheng Kang , Xin Jiang , Heng Yang

We present a faster interior-point method for optimizing sum-of-squares (SOS) polynomials, which are a central tool in polynomial optimization and capture convex programming in the Lasserre hierarchy. Let $p = \sum_i q^2_i$ be an…

Optimization and Control · Mathematics 2022-02-18 Shunhua Jiang , Bento Natura , Omri Weinstein

A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…

Symbolic Computation · Computer Science 2018-01-31 Haokun Li , Bican Xia

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…

Optimization and Control · Mathematics 2023-02-07 Junhyung Lyle Kim , JA Lara Benitez , Mohammad Taha Toghani , Cameron Wolfe , Zhiwei Zhang , Anastasios Kyrillidis

To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…

Optimization and Control · Mathematics 2024-02-05 Bo Yang , Xinyuan Zhao , Xudong Li , Defeng Sun

In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that…

Optimization and Control · Mathematics 2025-06-16 P. C. N. Verheijen , D. Goswami , M. Lazar

In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…

Optimization and Control · Mathematics 2022-12-29 Feng Guo , Meijun Zhang

In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…

Machine Learning · Computer Science 2021-06-04 Quanming Yao , Hangsi Yang , En-Liang Hu , James Kwok

We propose a new method for simplifying semidefinite programs (SDP) inspired by symmetry reduction. Specifically, we show if an orthogonal projection map satisfies certain invariance conditions, restricting to its range yields an equivalent…

Optimization and Control · Mathematics 2023-03-09 Frank Permenter , Pablo A. Parrilo

In this paper, a stochastic alternating direction method of multipliers (ADMM) is proposed for a class of nonsmooth composite and stochastic convex optimization problems in Hilbert space, motivated by optimization problems constrained by…

Optimization and Control · Mathematics 2026-05-18 Weihua Deng , Haiming Song , Hao Wang , Jinda Yang