PPT-A Combinatorial, Primal-Dual Approach to

Semidefinite Programming Satyen Kale Yahoo Research Joint work with Sanjeev Arora Princeton Semidefinite Programming Semidefinite Program SDP find X st . Houston TX 77005 sschaefericeedu and jwarrenriceedu Abstract We present a method for contouring an implicit function using a grid topologically dual to structured grids such as octrees By aligning the vertices of the dual grid with the features of t Daniel Tarlow. 1. , Dhruv . Batra. 2. . Pushmeet Kohli. 3. , Vladimir Kolmogorov. 4. 1: University of Toronto 3: Microsoft Research Cambridge. 2: TTI Chicago 4: University College London. . International Conference on Machine Learning (ICML), . Lecture 9. N. Harvey. http://www.math.uwaterloo.ca/~harvey/. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. A. A. A. Outline. Complementary Slackness. Sparse Approximations. Winter 2013. Lecture . 1. N. Harvey. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. A. A. A. Linear Program. Johnnie B. Linn . III. . Concord . University, Athens, WV. Creative Destruction as Industrial Mutation. The opening up of new markets, foreign or domestic, and the organizational development from the craft shop and factory to such concerns as U.S. Steel illustrate the same process of . Input: LP P in standard form with feasible . origo. .. Construct initial feasible dictionary D.. while. . some . has positive coefficient in z equation. Find a variable . which constrains increasing . 1. . . If x. i. . ≠ 0,. . i. = 1, 2, … , n the . ith. dual . equation is tight. .. 2. If . equation . i. of the primal . is not tight, . y. i. =0.. 1. Complementary Slackness Theorem (5.2): . Recall Toy . Example. Empirical . (Sample). EigenVectors. Theoretical. Distribution. & Eigenvectors. Different!. Connect Math to Graphics (Cont.). 2-d Toy Example. PC1 Projections. Best 1-d Approximations of Data. . Set Cover. Set Cover. Given. a universe . U . of. . n . elements. , . a collection of subsets of . U. , . S. = . {. S. 1. ,…,. . S. k. }, and a cost function . c. : . S. . → . Q. +. .. Find . Primal-dualsubgradientmethodminimizef0(x)subjecttofi(x)0;i=1;:::;mAx=bwithvariablex2Rn,fi:Rn!Rconvexprimal-dualsubgradientmethodupdatesbothprimalanddualvariablestheseconvergetoprimal-dualoptimalval Sahil. . Singla. . (Carnegie Mellon University). Joint work with . Aviad. Rubinstein. (18. th. Jan, 2017). Prophet Inequality. 2. Krengel. and . Sucheston. [. KS-BAMS’77]. Given. . distributions. Local Primal-Dual Gaps. Dhruv Batra (TTIC). Joint work with: . Daniel . Tarlow. (U Toronto), Sebastian . Nowozin. (MSRC), . Pushmeet. . Kohli. (MSRC), Vladimir . Kolmogorov. (UCL). Overview. Discrete . Given . network. . with . arc. . costs. . , . together. with balance . constraints. and . possibly. . arc. . constraints. .. Find . feasible. flow . minimizing.  . Solving. the minimum . cost. 1. A . cover. of an undirected graph . is a set . of nodes such that every . edge . of G has at least one end in . .. For any matching . and any cover . , each edge in . has an end in . and the corresponding nodes in C are all distinct..