PPT-Unconstrained Submodular

Unconstrained Submodular Maximization Moran Feldman The Open University of Israel Based On Maximizing Nonmonotone Submodular Functions Uriel Feige Vahab S Mirrokni and Jan Vondrák SIAM J. Tel Aviv University Tel Aviv Israel nivbuchbindergmailcom Moran Feldman Computer Science Dept Technion Haifa Israel moranfecstechnionacil Joseph Sef64257 Naor Computer Science Dept Technion Haifa Israel naorcstechnionacil Roy Schwartz Theory Group M 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 Submodular. Bandits Problem. Yisong Yue. Carnegie Mellon University. Joint work with Carlos Guestrin & Sue Ann Hong. Optimizing Recommender Systems. Must predict what the user finds interesting. . 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. Unconstrained (TRU) strategy is celebrating its 10-year anniversary. This gives Western Asset one of the longest track records in the growing unconstrained space. At the time of TRU’s inception, submodular. . objectives: . continuous extensions . &. . dependent . randomized . rounding. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Combinatorial Optimization. N. a finite ground set. . 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 . (x) = 0. h. i. (x) <= 0. Objective function. Equality constraints. Inequality constraints. Terminology. Feasible set. Degrees of freedom. Active constraint. classifications. Unconstrained v. constrained. Unconstrained minimization. Steepest descent vs. conjugate gradients. Newton and quasi-Newton methods. Matlab. . fminunc. Unconstrained local minimization. The necessity for one dimensional searches. Unconstrained minimization. Steepest descent vs. conjugate gradients. Newton and quasi-Newton methods. Matlab. . fminunc. Unconstrained local minimization. The necessity for one dimensional searches. 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), .