PPT-Approximation Algorithms for

Stochastic Optimization Anupam Gupta Carnegie Mellon University IPCO Summer School Approximation Algorithms for MultiStage Stochastic Optimization vertex cover S teiner tree MSTs. Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. Part I: Multistage problems. Anupam. Gupta. Carnegie Mellon University. stochastic optimization. Question: . How to model uncertainty in the inputs?. data may not yet be available. obtaining exact data is difficult/expensive/time-consuming. Raja . Giryes. ICASSP 2011. Volkan. Cevher. Agenda. The sparse approximation problem. Algorithms and pre-run guarantees. Online performance guarantees. Performance bound. Parameter selection. 2. Sparse approximation. Alexander . Veniaminovich. IM. , . room. . 3. 44. Friday. 1. 7. :00. or. Saturday 14:30. Approximation. . algorithms. . 2. We will study. . NP. -. hard optimization problem. 3. What you should know. Sometimes we can handle NP problems with polynomial time algorithms which are guaranteed to return a solution within some specific bound of the optimal solution. within a constant . c. . of the optimal. Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . Algorithms. and Networks 2015/2016. Hans L. . Bodlaender. Johan M. M. van Rooij. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. A. A. What to do if a problem is. Peter Andras. School of Computing and Mathematics. Keele University. p.andras@keele.ac.uk. Overview. High-dimensional functions and low-dimensional manifolds. Manifold mapping. Function approximation over low-dimensional projections. How accurate is your estimate?. Differential Notation. The Linear Approximation to . y. = . f. (. x. ) is often written using the “differentials” . dx. and . dy. . In this notation, . dx. is used instead of . When the best just isn’t possible. Jeff Chastine. Approximation Algorithms. Some NP-Complete problems are too important to ignore. Approaches:. If input small, run it anyway. Consider special cases that may run in polynomial time. Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. David P. Williamson. Joint work with Matthias Poloczek (Cornell), Georg Schnitger (Frankfurt), and Anke van Zuylen (William & Mary). Greedy algorithms. “Greed. , for lack of a better word, is good. Greed is right. Greed works. 10 Bat Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, 2014 The bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010. 10.1 Echolocation of Bats Lecture 18. May 29, . 2014. May 29, 2014. 1. CS38 Lecture 18. May 29, 2014. CS38 Lecture 18. 2. Outline. coping with . intractibility. approximation algorithms. set cover. TSP. center selection. randomness in algorithms.