Reduction methods in semidefinite and conic optimization

Conic optimization, or cone programming, is a subfield of convex optimization that includes linear, second-order cone, and semidefinite programming as special cases. While conic optimization problems arise in a diverse set of fields (including machine learning, robotics, and finance), efficiently solving them remains an active area of research. Developing methods that detect and exploit useful structure-such as symmetry, sparsity, or degeneracy-is one research topic. Such methods include facial and symmetry reduction, which have been successful in several applications, often reducing solve time by orders of magnitude. Nevertheless, theoretical and practical barriers preclude their general purpose use: to our knowledge, no solver uses facial or symmetry reduction as an automatic preprocessing step. This thesis addresses some of these barriers in three parts: the first develops more practical facial reduction techniques, the second proposes a more powerful and computationally efficient generalization of symmetry reduction (which we call Jordan reduction), and the third specializes techniques to convex relaxations of polynomial optimization problems. Throughout, we place emphasis on semidefinite programs and, more generally, optimization problems over symmetric cones. We also present computational results.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Permenter, Frank Noble

Advisor dc:contributor.advisor

• Pablo A. Parrilo and Russ Tedrake.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/114005

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/114005