Convex Conic Optimization, Applications, Modeling Languages, and Solvers

Convex conic linear optimization problems are an extension of linear programming with linear objectives, linear constraints, and additional conic constraints.  These conic constraints require feasible solutions to lie within cones such as the nonnegative orthant (linear programming) or the cone of positive semidefinite matrices (semidefinite programming.)  In recent years, research in this area has expanded beyond LP and SDP to include additional "exotic" cones. There are now open source and commercial solvers that can solve a wide range of problems.  There are also modeling systems that can automatically convert optimization problems into conic form and solve them using a variety of solvers.  In this talk, I'll review the basic theory of conic optimization, describe some applications and their conic formulations, and discuss software packages for modeling and solving convex conic optimization problems.

http://euler.nmt.edu/~brian/