Semidefinite Programming

Also known as SDP

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Following a Unique Path: A Fast Certifier Applied to Outlier-Robust Pose Registration
Sep 2, 2026Connor Holmes, Abhishek Goudar, Timothy D. BarfootSemidefinite Programming Point Cloud Registration
University of Toronto Robotics Institute, University of Toronto, Toronto, Ontario, Canada
Semidefinite Relaxations for Collision-Free Motion Planning
Jun 12, 2026Bernhard Paus Graesdal, Alexandre Amice, Pablo A. Parrilo +1Semidefinite Programming Constrained Motion Planning
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.
Scalable Deep Unfolding of Conic Optimizers
Jun 11, 2026Alex Oshin, Rahul Vodeb Ghosh, Evangelos A. TheodorouSemidefinite Programming Algorithm Unrolling
Georgia Institute of Technology
Conditioned free-energy density of proteins using unbalanced solutions to constraint satisfaction problems
May 31, 2026Pratik Worah, Subhash Khot, Srinivasa VaradhanFree Energy Calculation Semidefinite Programming
Exploiting Chordal Sparsity for Globally Optimal Estimation with Factor Graphs
May 28, 2026Avinash Subramanian, Connor Holmes, Timothy D. Barfoot +2Semidefinite Programming Factor Graph Optimization
College of Computing, Georgia Institute of Technology, Atlanta, GA, USA · Robotics Institute, University of Toronto, Toronto, ON, Canada · Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA
TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics
May 13, 2026Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo +4Semidefinite Programming Constrained Motion Planning
Columbia University, USA · Massachusetts Institute of Technology, USA · ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Switzerland +1
Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networks
May 8, 2026Hao Chen, Chendi Qian, Christopher Morris +2Semidefinite Programming Graph Neural Networks
1Davidson School of Chemical Engineering, Purdue University · Faculty of Computer Science, RWTH Aachen University · 3Jacobs Technion-Cornell Institute, Cornell Tech
Globally Solving Unbalanced Optimal Transport and Density Control for Gaussian Distributions
May 5, 2026Haruto Nakashima, Siddhartha Ganguly, Kenji KashimaSemidefinite Programming Stochastic Optimal Control
The Applied Mathematics and Physics Department, Graduate School of Informatics, Kyoto University, Kyoto, Japan · Daniel Guggenheim School of Aerospace, Georgia Institute of Technology, Atlanta, USA
On the Expressive Power of GNNs to Solve Linear SDPs
Apr 30, 2026Chendi Qian, Christopher MorrisSemidefinite Programming Graph Neural Networks
Faculty of Computer Science, RWTH Aachen University, Germany
Mixtures Closest to a Given Measure: A Semidefinite Programming Approach
Sep 26, 2025Srećko Đurašinović, Jean-Bernard Lasserre, Victor MagronSemidefinite Programming Data Mixture Optimization
College of Computing and Data Science, NTU, Singapore · LAAS-CNRS, Toulouse, France · Toulouse School of Economics +1
Semidefinite programming relaxations and debiasing for MAXCUT-based clustering
Jan 16, 2024Shuheng ZhouSemidefinite Programming Unsupervised Clustering
University of California, Riverside, CA 92521
Semidefinite Programming for Quantum Channel Learning
Date pendingMikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov +3Semidefinite Programming Quantum Machine Learning
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, GSP-1, Moscow, Vorob’evy Gory, 119991, Russia and Autretech Group, Skolkovo Innovation Center, Nobel Street, Building 7, Moscow, 121205, Russia · Peter the Great St. Petersburg Polytechnic University, 195251, Russia · Ioffe Institute, Politekhnicheskaya 26, St Petersburg, 194021, Russia

Sep 2, 2026, cs.ROJ/K move · Enter open · S save

Following a Unique Path: A Fast Certifier Applied to Outlier-Robust Pose Registration

Connor Holmes, Abhishek Goudar, Timothy D. Barfoot

University of Toronto Robotics Institute, University of Toronto, Toronto, Ontario, Canada

Semidefinite Programming Point Cloud Registration

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Certifiable methods have arisen as a means to guarantee global optimality of solutions to non-convex problems using convex semidefinite programming (SDP) relaxations. The most performant of these methods use a local solver to obtain the candidate solution, and then certify its optimality using efficient linear algebra techniques. However, for many problems of interest in robotics, this local-solve-then-certify approach is impeded by a form of degeneracy in the relaxation, leaving a costly optimization of the relaxation as the only recourse. In this paper, we introduce our Central-Path Certifier (CP-Cert), a certifiable method explicitly tailored to certify candidate optima to problems that exhibit this form of degeneracy. Using a candidate as a starting point, our approach seeks a nearby region of the feasible space -- known as the central path -- where a valid certificate can be readily obtained. The approach is kept efficient by exploiting indirect linear algebra techniques, problem sparsity, and parallelism. We apply CP-Cert to both matrix-weighted pose registration and pointcloud data association, whose novel SDP relaxation is of independent interest. On simulated examples, we explore the properties of this novel relaxation and show that CP-Cert is fast and scalable, achieving runtimes that are up to three orders of magnitude faster than state-of-the-art direct solvers. Finally, we combine these contributions into a certifiable, outlier-robust pose-estimation pipeline, which we apply to real-world data.

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