PPT-Understanding the Power of Convex Relaxation Hierarchies:

Effectiveness and Limitations Yuan Zhou Computer Science Department Carnegie Mellon University 1 Combinatorial Optimization Goal optimize an objective function of n 01 variables Subject to . T his problem named optimal power 64258ow OPF is nonconvex due to the nonlinearities imposed by the laws of physics and has been studied since 1962 We have recently shown that a convex relaxation based on semide64257nite programming SDP is able t 64 1HANDMAIDENS, HIERARCHIES, AND CROSSING THE PUBLIC-PRIVATE DIVIDE IN THETEACHING OF INTERNATIONAL LAWDianne OttoI want to address the question of what law students are encouraged to imagine is the rol Effectiveness and Limitations. Yuan Zhou. Computer Science Department. Carnegie Mellon University. 1. Combinatorial Optimization. Goal:. optimize an objective function of . n. 0-1 variables. Subject to: . Nonconvex Polynomials with . Algebraic . Techniques. Georgina . Hall. Princeton, ORFE. Joint work with . Amir Ali Ahmadi. Princeton, ORFE. 1. 7/13/2015. MOPTA . 2015. Difference of Convex (DC) programming. Tensor Decomposition and Clustering. Moses . Charikar. Stanford University. 1. Rich theory of analysis of algorithms and complexity founded on worst case analysis. Too pessimistic. Gap between theory and practice. relaxations. via statistical query complexity. Based on:. V. F.. , Will Perkins, Santosh . Vempala. . . On the Complexity of Random Satisfiability Problems with Planted . Solutions.. STOC 2015. V. F.. Haggai . Maron, . Nadav. . Dym. , . . Itay. . Kezurer. , . . Shahar. . Kovalsky. , . . Yaron. . Lipman. . Weizmann . Institute of Science. 1. Orthogonal.  .  .  .  . Orthogonal Procrustes Problem. general . submodular. functions. CVPR 2015 . Tutorial. Stefanie Jegelka. MIT. The set function view. 2. cost. of buying items . together, or. utility, . or. probability, …. (. . ). Flow. Manuel Ruiz – RTE – manuel.ruiz@rte-france.com. 1. 2. A . small. . example. . The power system network is a graph described . using . buses (nodes) and branches (directed edges). . Power flow computations aim at providing a power and voltage distribution of a power system network given . Columbia . University. . Graph-Theoretic Algorithm for Arbitrary Polynomial Optimization Problems with Applications to Distributed Control, Power Systems, and Matrix Completion. . Joint work with. :. Senior Program Manager. Master Data Services. Microsoft Corporation. Microsoft . SQL Server 2012. ®. ®. Agenda. Introduction to Hierarchies. Level Based vs. Ragged Hierarchies. Derived Hierarchies. M. Pawan Kumar. Slides available online http://. mpawankumar.info. Energy Function. V. a. V. b. V. c. V. d. Label . l. 0. Label . l. 1. Random Variables V. . = {V. a. , V. b. , ….}. Labels L. . = {l. M. Pawan Kumar. pawan.kumar@ecp.fr. Slides available online http://. cvn.ecp.fr. /personnel/. pawan. Recap. V. a. V. b. V. c. d. a. d. b. d. c. Label . l. 0. Label . l. 1. D. : Observed data (image). . III. Relaxation. . techniques. Relaxation. . techniques. Relaxation techniques can reduce stress symptoms and help you enjoy a better quality of life, especially if you have an illness. . Relaxation techniques are a great way to help with...