Reception to follow.
We describe conic geometric programs (CGPs), which are convex optimization problems obtained by blending elements of geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective function that is to be minimized subject to affine constraints, convex conic constraints, and upper bound constraints on sums of exponential and affine functions. Although CGPs contain GPs and SDPs as special instances, computing global optima of CGPs is not much harder than solving GPs and SDPs. More broadly, the CGP framework facilitates a range of new applications that fall outside the scope of SDPs and GPs alone. We demonstrate the utility of CGPs in providing solutions to problems such as (i) permanent maximization, (ii) hitting-time estimation in dynamical systems, (iii) the computation of the capacity of channels transmitting quantum information, (iv) tractable robust optimization formulations of GPs, and (v) the computation of bounds for nonconvex "signomial" programs. (Joint work with Parikshit Shah.)
Venkat Chandrasekaran is an Assistant Professor at Caltech in Computing and Mathematical Sciences and in Electrical Engineering. He received a Ph.D. in Electrical Engineering and Computer Science in June 2011 from MIT, and he received a B.A. in Mathematics as well as a B.S. in Electrical and Computer Engineering in May 2005 from Rice University. He was awarded the Jin-Au Kong Dissertation Prize for the best doctoral thesis in Electrical Engineering at MIT (2012), the Young Researcher Prize in Continuous Optimization at the Fourth International Conference on Continuous Optimization of the Mathematical Optimization Society (2013), an Okawa Research Grant in Information and Telecommunications (2013), and the NSF Career award (2014). His research interests lie in mathematical optimization and its application to the information sciences.