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Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…

Data Structures and Algorithms · Computer Science 2020-08-07 Nai-Hui Chia , Tongyang Li , Han-Hsuan Lin , Chunhao Wang

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

Optimization and Control · Mathematics 2025-10-15 Zilong Cui , Ran Gu

We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a…

Optimization and Control · Mathematics 2022-08-08 Samuel Burer , Kyungchan Park

We study the ternary quadratic problem (TQP), a quadratic optimization problem with linear constraints where the variables take values in $\{0, \pm 1\}$. While semidefinite programming (SDP) techniques are well established for $\{0,1\}$-…

Optimization and Control · Mathematics 2026-04-01 Frank de Meijer , Veronica Piccialli , Renata Sotirov , Antonio M. Sudoso

Quadratic Unconstrained Binary Optimization (QUBO) problems are prevalent in various applications and are known to be NP-hard. The seminal work of Goemans and Williamson introduced a semidefinite programming (SDP) relaxation for such…

Quantum Physics · Physics 2025-10-10 Haomu Yuan , Daniel Stilck França , Ilia Luchnikov , Egor Tiunov , Tobias Haug , Leandro Aolita

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

Optimization and Control · Mathematics 2024-03-19 Yifan Ran , Stefan Vlaski , Wei Dai

This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial programs in the face of data uncertainty. The class of convex programs, called robust SOS-convex programs, includes…

Optimization and Control · Mathematics 2014-03-05 V. Jeyakumar , G. Li , J. Vicente-Perez

For nonconvex quadratically constrained quadratic programs (QCQPs), we first show that, under certain feasibility conditions, the standard semidefinite (SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact optimal…

Optimization and Control · Mathematics 2022-05-03 Godai Azuma , Mituhiro Fukuda , Sunyoung Kim , Makoto Yamashita

In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We…

Information Theory · Computer Science 2024-03-06 Gastón De Boni Rovella , Meryem Benammar

A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding…

Machine Learning · Computer Science 2023-03-30 Zenan Ling , Xingyu Xie , Qiuhao Wang , Zongpeng Zhang , Zhouchen Lin

Matching problems on 3D shapes and images are challenging as they are frequently formulated as combinatorial quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. In this work, we address such problems…

Computer Vision and Pattern Recognition · Computer Science 2021-07-09 Marcel Seelbach Benkner , Vladislav Golyanik , Christian Theobalt , Michael Moeller

Quadratic assignment problem (QAP) is a fundamental problem in combinatorial optimization and finds numerous applications in operation research, computer vision, and pattern recognition. However, it is a very well-known NP-hard problem to…

Optimization and Control · Mathematics 2024-08-13 Shuyang Ling

The concept of Generalized Inverse based Decoding (GID) is introduced, as an algebraic framework for the syndrome decoding problem (SDP) and low weight codeword problem (LWP). The framework has ground on two characterizations by generalized…

Information Theory · Computer Science 2022-02-18 Ferucio Laurentiu Tiplea , Vlad-Florin Dragoi

In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The infinite-dimensional optimal control problem is reduced into a…

Optimization and Control · Mathematics 2023-03-06 Kareem T. Elgindy

Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…

Quantum Physics · Physics 2023-10-13 Oscar Watts , Yuta Kikuchi , Luuk Coopmans

Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without…

Information Theory · Computer Science 2013-02-19 Badri Narayan Bhaskar , Gongguo Tang , Benjamin Recht

We give new rounding schemes for SDP relaxations for the problems of maximizing cubic polynomials over the unit sphere and the $n$-dimensional hypercube. In both cases, the resulting algorithms yield a $O(\sqrt{n/k})$ multiplicative…

Data Structures and Algorithms · Computer Science 2023-10-03 Jun-Ting Hsieh , Pravesh K. Kothari , Lucas Pesenti , Luca Trevisan

Decoding sparse quantum codes can be accomplished by syndrome-based decoding using a belief propagation (BP) algorithm.We significantly improve this decoding scheme by developing a new feedback adjustment strategy for the standard BP…

Quantum Physics · Physics 2013-09-25 Yun-Jiang Wang , Barry C. Sanders , Bao-Ming Bai , Xin-Mei Wang

We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the…

Optimization and Control · Mathematics 2025-08-05 Ahmad Al-Sulami , Hamza Fawzi , Shengding Sun

We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…

Computational Complexity · Computer Science 2014-11-25 James R. Lee , Prasad Raghavendra , David Steurer