Title: Exploiting Special Structures in Conic Optimization

Conic optimization (CO) problems provide a rich and unifying framework for the theoretical and computational study of a variety of optimization problems such as linear programming, second-order cone programming, and semidefinite programming problems. However, natural formulations of many CO problems do no fit the standard form of this problem or its dual used in implementations and therefore, to solve such problems using the available software one often needs to reformulate these problems by introducing new variables and/or constraints.
In this talk, we discuss some of the most frequently encountered structures in reformulation of non-standard form CO problems into standard form CO problems and introduce computational techniques that provide special handling of such structures for improved performance and accuracy. In particular, we discuss problems with unrestricted variables, fixed variables, cone intersection constraints, and quadratic objectives. We also present computational results obtained by the implementation of these ideas in the new version of SDPT3, a MATLAB-based software package.