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Historically, scalability has been a major challenge to the successfulapplication of semidefinite programming in fields such as machine learning,control, and robotics. In this paper, we survey recent approaches foraddressing this challenge including (i) approaches for exploiting structure(e.g., sparsity and symmetry) in a problem, (ii) approaches that producelow-rank approximate solutions to semidefinite programs, (iii) more scalablealgorithms that rely on augmented Lagrangian techniques and the alternatingdirection method of multipliers, and (iv) approaches that trade off scalabilitywith conservatism (e.g., by approximating semidefinite programs with linear andsecond-order cone programs). For each class of approaches we provide ahigh-level exposition, an entry-point to the corresponding literature, andexamples drawn from machine learning, control, or robotics. We also present alist of software packages that implement many of the techniques discussed inthe paper. Our hope is that this paper will serve as a gateway to the rich andexciting literature on scalable semidefinite programming for both theorists andpractitioners.

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics