PPT-Convex Optimization

for Sequential Game Solving Overview Sequenceform transformation Bilinear saddlepoint problems EGTMirror prox Smoothing techniques for sequential games Sampling techniques Some experimental results. The following are equivalent is PSD ie Ax for all all eigenvalues of are nonnegative for some real matrix Corollary Let be a homogeneous quadratic polynomial Then for all if and only if for some Rudi Pendavingh TUE Semide64257nite matrices Con Consider all possible pairs of points in the set and consider the line segment connecting any such pair. All such line segments must lie entirely within the set.. Convex Set of Points. Convex –vs- Nonconvex. Given a set of points (x. 1. ,y. 1. ),(x. 2. ,y. 2. ),…,(x. n. ,y. n. ), the . convex hull. is the smallest convex polygon containing all the points.. Convex Hulls. Given a set of points (x. 1. ,y. Northeastern University. Yongfang. Cheng. 1. , Yin Wang. 1. , Mario Sznaier. 1. , . Necmiye. Ozay. 2. , . Constantino. M. Lagoa. 3. 1. Department of Electrical and Computer Engineering. Northeastern University, Boston, MA, USA. 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. 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.. Guo. . Qi, . Chen . Zhenghai. , Wang . Guanhua. , Shen . Shiqi. , . Himeshi. De Silva. Outline. Introduction: Background & Definition of convex . hull. Three . algorithms. Graham’s Scan. Jarvis March. machine learning. Yuchen Zhang. Stanford University. Non-convexity . in . modern machine learning. 2. State-of-the-art AI models are learnt by minimizing (often non-convex) loss functions.. T. raditional . 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.. Sinusoidal Modeling . for. . Audio . Signal Processing. Michelle Daniels. PhD Student, University of California, San Diego. Outline. Introduction to sinusoidal . modeling. Existing approach. Proposed optimization post-processing. Partially Based on WORK FROM Microsoft Research With:. 1. 1, 3. 4-->5. 1: MSR Redmond 2: Weizmann Institute 3: University of Washington 4: Stanford 5: CMU. Sébastien Bubeck, Bo’az Klartag, Yin Tat Lee, Yuanzhi Li. Motivation and IntroductionHow to employ data for optimal control? Plant DisturbanceInputController CostsConstraints State •Model-Free RL simultaneously parameterize -Poor data efficiency-Dynamic Date Monday June 17 2013 till Thursday June 20 2013TimeVenue Included 2 Co31ee Breaks and a Lunch EE Short CourseTopics to be CoveredDue to the limited space RSVP is required byemailing the local coo Xinyuan Wang. 01/. 17. /20. 20. 1. Contents. Affine. . and. . convex. . sets. Example. . of. . convex. . sets. Key. . properties. . of. . convex. . sets. Proper . cone, dual cone and . generalized .