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Cluster :  Conic Programming

Session Information  : Wednesday Jul 15, 14:45 - 16:15

Title:  Convex Conic Optimization: Models, Properties, and Algorithms II
Chair: Farid Alizadeh,Professor, Rutgers University, MSIS department, 100 Rockefallar, room 5142, Piscataway NJ 08854, United States of America, alizadeh@rci.rutgers.edu

Abstract Details

Title: DSOS and SDSOS: More Tractable Alternatives to Sum of Squares and Semidefinite Programming
 Presenting Author: Anirudha Majumbar,MIT, MIT 32-380 Vassar Street, Cambridge, United States of America, anirudha@mit.edu
 Co-Author: Amir Ali Ahmadi,Princeton University, a_a_a@princeton.edu
 Russ Tedrake,MIT, russt@mit.edu
 
Abstract: Sum of squares optimization has undoubtedly been a powerful addition to the theory of optimization in the past decade. Its reliance on relatively large-scale semidefinite programming, however, has seriously challenged its ability to scale in many practical applications. In this presentation, we introduce DSOS and SDSOS optimization as more tractable alternatives to sum of squares optimization that rely instead on LP and SOCP. We show that many of the theoretical guarantees of sum of squares optimization still go through for DSOS and SDSOS optimization. Furthermore, we show with numerical experiments from diverse application areas that we can handle problems at scales that are currently far beyond reach for sum of squares approaches.
  
Title: An Improved Bound for the Lyapunov Rank of a Proper Cone
 Presenting Author: Muddappa Gowda,Professor of Mathematics, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore MD 21250, United States of America, gowda@umbc.edu
 Co-Author: Michael Orlitzky,University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore MD 21250, United States of America, mjo@umbc.edu
 
Abstract: The Lyapunov rank (also called the bilinearity rank) of a proper cone in an n-dimensional real inner product space is the number of linearly independent Lyapunov-like linear transformations (also called bilinearity relations) needed to express its complementarity set. Such a set arises, for example, in conic optimization in the form of optimality conditions. In any symmetric cone (such as the nonnegative orthant or the semidefinite cone), the rank is at least the dimension of the ambient space and the complementarity set can be described by a square system of independent bilinear relations. With the goal of seeking such `perfect' cones, in this talk, we describe an improved bound for the Lyapunov rank.
  
Title: On a Generalized Second Order Cone
 Presenting Author: Roman Sznajder,Professor, Bowie State University, 14000 Jericho Park Road, Bowie Ma 20715, United States of America, RSznajde@bowiestate.edu
 
Abstract: In this paper, we study various properties of a generalized second order cone, considered as a multivariate version of topheavy cone with respect to arbitrary norm in a Euclidean space. Among other properties, we investigate the structure of Lyapunov-like transformations on such a cone and compute its Lyapunov rank.