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Subsampling algorithms for semidefinite programming [PDF]
Stochastic Systems, 2011 We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls granularity, i.e.
Alexandre W. d'Aspremont
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HBSP: a hybrid bilinear and semidefinite programming approach for aligning partially overlapping point clouds [PDF]
Scientific ReportsIn many applications, there is a need for algorithms that can align partially overlapping point clouds while remaining invariant to corresponding transformations.
Wei Lian, Fei Ma, Zhesen Cui, Hang Pan
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Scalable Semidefinite Programming [PDF]
SIAM Journal on Mathematics of Data Science, 2021 Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs.
Alp Yurtsever +4 more
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Quantum key distribution rates from semidefinite programming [PDF]
Quantum, 2023 Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases.
Mateus Araújo +4 more
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Numerical algebraic geometry and semidefinite programming
Results in Applied Mathematics, 2021 Standard interior point methods in semidefinite programming can be viewed as tracking a solution path for a homotopy defined by a system of bilinear equations.
Jonathan D. Hauenstein +3 more
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Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming
Mathematics, 2023 The systematic design of exact optimal designs of experiments is typically challenging, as it results in nonconvex optimization problems. The literature on the computation of model-based exact optimal designs of experiments via mathematical programming ...
Belmiro P. M. Duarte
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Semidefinite Programming and Ramsey Numbers [PDF]
SIAM Journal on Discrete Mathematics, 2021 Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed to find asymptotic results for very large graphs, so it seems that the method is not suitable for finding small Ramsey numbers. But this intuition is wrong, and we will develop a technique to do just that in this paper.
Bernard Lidický, Florian Pfender
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Enhancing pseudo-telepathy in the magic square game. [PDF]
PLoS ONE, 2013 We study the possibility of reversing an action of a quantum channel. Our principal objective is to find a specific channel that reverses as accurately as possible an action of a given quantum channel. To achieve this goal we use semidefinite programming.
Lukasz Pawela +3 more
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Time-Varying Semidefinite Programs [PDF]
Mathematics of Operations Research, 2021 We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data vary polynomially with time. We show that under a strict feasibility assumption, restricting the solutions to also be polynomial functions of time does not change the ...
Amir Ali Ahmadi, Bachir El Khadir
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Entropy-Penalized Semidefinite Programming [PDF]
Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, 2019 Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts.
Mikhail Krechetov +3 more
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