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This paper proposes a squared smoothing Newton method via the Huber smoothing function for solving semidefinite programming problems (SDPs). We first study the fundamental properties of the matrix-valued mapping defined upon the Huber…

Optimization and Control · Mathematics 2024-10-10 Ling Liang , Defeng Sun , Kim-Chuan Toh

This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…

Optimization and Control · Mathematics 2021-11-22 Baihe Huang , Shunhua Jiang , Zhao Song , Runzhou Tao , Ruizhe Zhang

Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…

Systems and Control · Electrical Eng. & Systems 2024-10-01 Zhaojun Ruan , Libao Shi

It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…

Optimization and Control · Mathematics 2023-11-09 Frank de Meijer , Renata Sotirov

We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us…

Data Structures and Algorithms · Computer Science 2023-09-12 Zhao Song , Mingquan Ye , Lichen Zhang

HDSDP is a numerical software solving the semidefinite programming problems. The main framework of HDSDP resembles the dual-scaling interior point solver DSDP [BY2008] and several new features, including a dual method based on the…

Mathematical Software · Computer Science 2023-11-10 Wenzhi Gao , Dongdong Ge , Yinyu Ye

Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…

Optimization and Control · Mathematics 2022-05-11 Pedro Abdalla , Afonso S. Bandeira

Running machine learning analytics over geographically distributed datasets is a rapidly arising problem in the world of data management policies ensuring privacy and data security. Visualizing high dimensional data using tools such as…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-11-13 Viska Wei , Nikita Ivkin , Vladimir Braverman , Alexander Szalay

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

Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…

Quantum Physics · Physics 2023-06-21 Paul Skrzypczyk , Daniel Cavalcanti

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

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

Optimization and Control · Mathematics 2020-06-19 Lijun Ding , Alp Yurtsever , Volkan Cevher , Joel A. Tropp , Madeleine Udell

Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity…

Machine Learning · Computer Science 2019-11-26 Lingfei Wu , Pin-Yu Chen , Ian En-Hsu Yen , Fangli Xu , Yinglong Xia , Charu Aggarwal

The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

Optimization and Control · Mathematics 2019-08-09 Elisabeth Gaar , Franz Rendl

We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…

Machine Learning · Computer Science 2014-02-25 Yan Yan , Chunhua Shen , Hanzi Wang

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

Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…

Optimization and Control · Mathematics 2022-02-28 Biel Roig-Solvas , Mario Sznaier

We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson\hyp{}Lindenstrauss transforms to produce a smaller SDP whose solution preserves feasibility or…

Optimization and Control · Mathematics 2019-02-12 Andreas Bluhm , Daniel Stilck Franca

The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP)…

Machine Learning · Computer Science 2016-03-17 Arash A. Amini , Elizaveta Levina

We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are…

Information Theory · Computer Science 2025-06-24 Julia Gaudio , Phawin Prongpaophan