Tutte Colloquium - Mehdi Karimi

Title: Convex Optimization Problems in Domain-Driven Form

Abstract:

In this talk, we introduce the Domain-Driven form for convex optimization problems and show how general it is by several examples; including LP, SDP, geometric and entropy programming, and quantum entropy optimization. We have designed infeasible-start primal-dual interior-point algorithms for the Domain-Driven form.  Our developed duality theory for this form, which accepts both conic and non-conic constraints, lets our techniques enjoy many advantages of primal-dual interior-point techniques available for conic formulations, such as the current best complexity bounds. We briefly talk about the geometry of convex optimization problems given in a Domain-Driven form and categorize possible statuses of these problems using duality theory. Our methods determine and certify these statuses as rigorously as the best approaches for conic formulations (which have been demonstrably very efficient in this context). At the end, we introduce our software package DDS created based on our results and talk about the numerical challenges and future potentials. 

This is a joint work with Levent Tuncel.