DSOS and SDSOS Optimization: LP and SOCP-Based Alternatives to Sum of Squares Optimization

Sum of squares (SOS) optimization has been a powerful and influential addition to the theory of optimization in the past decade. Its reliance on relatively large-scale semidefinite programming, however, has seriously challenged its ability to scale in many practical applications. In this paper, we introduce DSOS and SDSOS optimization1 as more tractable alternatives to sum of squares optimization that rely instead on linear programming and second order cone programming. These are optimization problems over certain subsets of sum of squares polynomials and positive semidefinite matrices and can be of potential interest in general applications of semidefinite programming where scalability is a limitation.

Note: This is an invited paper for the session on “Optimization in the Information Sciences” of the 48th Annual Conference on Information Sciences and Systems (CISS 2014). It is meant to serve as an extended abstract for a longer upcoming paper [1] by the authors on the same topic. Most details are omitted.

By: Amir Ali Ahmadi, Anirudha Majumdar

Published in: Proceedings of 2014 48th Annual Conference on Information Sciences and Systems (CISS),Piscataway, NJ, , IEEE. , p.10.1109/CISS.2014.6814141 in 2014


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