PPT-Provable Submodular Minimization

using Wolfes Algorithm Deeparnab Chakrabarty Microsoft Research Prateek Jain Microsoft Research Pravesh Kothari U Texas Submodular Functions f Subsets of 12n integers. 2 Standard Minimization Problems Minimization with constraints Example Solve the linear programming problem minimize 4 2 2 10 4 12 xyz Standard Minimization Problems 1 Objective function is minimized 2 All variables are nonnegative 3 All constrai washingtonedu Jeff Bilmes Department of Electrical Engineering University of Washington bilmesuwashingtonedu Abstract We investigate two new optimization problems minimizing a submodular function subject to a submodular lower bound constraint submod . Tripathi. Georgia Institute of Technology. Approximability. of Combinatorial Optimization Problems with . Submodular. Cost Functions. Based on joint work with . Gagan. . Goel. , . Chinmay. . Karande. Lecture 5 – Part 1. M. Pawan Kumar. pawan.kumar@ecp.fr. Slides available online http://. cvn.ecp.fr. /personnel/. pawan. /. Submodular. Functions. Examples. Outline. Submodular. Function. Set S. Function f over power set of S. . Defaults. Foundations of AI. Given an N X N matrix, and given N colors, color the matrix in such a way that:. -all cells are colored;. - each color occurs exactly once in each row;. - each color occurs exactly once in each column;. submodular. . objectives: . continuous extensions . &. . dependent . randomized . rounding. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Combinatorial Optimization. N. a finite ground set. . Defaults. Foundations of AI. Given an N X N matrix, and given N colors, color the matrix in such a way that:. -all cells are colored;. - each color occurs exactly once in each row;. - each color occurs exactly once in each column;. Reading Group. Submodular. Function Minimization. via Linear Programming. M. Pawan Kumar. http://. www.robots.ox.ac.uk. /~oval/. Separation and Optimization. Submodular. Function Minimization. Outline. . for Binary . Pairwise. Energies. Lena . Gorelick. . joint work with. . O. . Veksler. I. Ben . Ayed. A. Delong. . Y. . Boykov. Example of Simple Binary Energy. 2. Potts Model. Binary . Pairwise. Dictionary Selection. for Sparse Representation. Volkan . Cevher. volkan.cevher@epfl.ch. Laboratory. for Information . . and Inference Systems - . LIONS. & . Idiap. Research Institute. . Joint work with . Deborah Gore. PERCS Unit. December 17, 2013. Background. Statewide TMDL for HG. Statewide fish consumption advisory. 67% reduction from 2002 baseline. The waters have moved to Category 4. 2% of Hg from point sources. . PAGE 138 to 142. . fact. An objective statement, one that can be proved . opinion. One possible interpretation of the facts, subjective statement that is not based on proof . Objective. Provable . Approximability. of Combinatorial Optimization Problems with . Submodular. Cost Functions. Based on joint work with . Gagan. . Goel. , . Chinmay. . Karande. , and Wang Lei. Motivation . Network Design Problem. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. Maria . Florina. . Balcan. LGO, . 11/16/2010. f(S)+f(T) . ¸. f(S . Å. T) + f(S . [. T), .