Table of Contents
Optimization (24h, 3 ECTS)Responsible : Spyros Angelopoulos (CNRS and Paris Sorbonne) HandoutsInstructors
Related CoursesThe following is a list of courses related to the topics of Algorithms and Complexity. ObjectiveThe objective of this course is to give an overview of the main techniques used in optimization, with emphasis on mathematical programming. For the 2018 offering of this course, the course will focus on decisionmaking aspects of optimization, and in particular, optimization in the presence of uncertainty. We will study topics that cover certain aspects of online optimization, learning, and stochastic optimization. Course lectures[Sep 17] Linear programming (brief intro), duality, simplex [DPV: 7:1, 7:4, 7:6], duality and optimality: shortest path [WS: 7.3]. [Sep 24] Simple rounding for vertex cover, integrality gap, duality and approximability [V: 12], primaldual for vertex cover, a sophisticated rounding for the generalized load balancing problem [KT: 11.7]. [Oct 1] The Maximum Value problem. An 8approximation using LProunding. Stochastic matchings. This follows Chapter 1 in [Mun2018] (see references). [Oct 8] A 3approximation for the Maximum Value problem using Lagrangian relaxation. Prophet inequality. This follows chapters 2.1, 2.2 in [Mun2018]. [Oct 15] Submodular functions (sections 3.1, 3.2 in [Mun2018]). Separation oracles and the ellipsoid method (briefly discussed, see, e.g., Section 4.3 in [WS 2011]). [Oct 22] Set cover via dual fitting (section 4.1. in [Mun 2018]). The ski rental problem (see Section 3 in this survey by Buchbinder and Naor, also covered in Chapter 13 in [Mun2018]). [Oct 29] The Multiplicative Weight Update algorithm [AM] (see also in this survey by Arora et al.). Application to the solution of covering linear programs [OS]. [Nov 5] Online learning and its relation with the Metrical Task System problem (based on this paper by Blum and Burch). HomeworksHomework 1 (due on October 8). Homework 2 (due on October 15). Homework 3 (due on October 22). Homework 4 (due on October 29). Homework 5 (due on November 5). Homework 6 (due on November 16). Grading scheme, presentations, and homework policyThere will be homeworks (25%), a class presentation (25%) and a final exam (50%). The presentations will be done during class on November 12. Please refer to the email for instructions. Homework policy: you should not search for solutions on the internet. If, for some reason, you ended up using outside help, you must cite your sources. No collaboration among students is allowed. All homeworks will be due on the beginning of the class. We will not accept late homeworks. The course exam will be on Monday, Nov 19, in the same room as the lectures. The exam is closedbook, but you can bring a single A4sized page with your notes. You can use only one side of the page. PapersThe following is a list of suggested papers for class presentation:
InternshipWe will propose internships early in the course offering. We urge all students who are interested to talk with the instructors as soon as possible. The internships will be related to the topics of research of the instructors and the lectures given in the course, or, more broadly, to the research interests of the instructors. Posted internships: References
