Abstract:

Homogeneous cone optimization (a.k.a. linear optimization over homogeneous cones) is an extension of linear optimization where all linear inequality constraints are replaced by a linear conic constraint involving a homogeneous cone. While it is a large class of optimization problems that includes semidefinite optimization and convex quadratic optimization (and much more), homogeneous cone optimization is almost never used in practice for two reasons: 1) all homogeneous cone optimization problems can be modeled, hence solved, as semidefinite optimization problems, and 2) there is a lack of development of primal-dual algorithms for homogeneous cone optimization. In this talk, I will present some interesting practical optimization problems that can be naturally modeled by homogeneous cone optimization. This will be followed with a presentation of recent results that are directly related to the development primal-dual algorithms for homogeneous cone optimization.