相关论文: Fast, Scalable, Warm-Start Semidefinite Programmin…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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…

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)…

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…