Robust optimization lecture notes

Robust optimization bdc 62189 lecture 1 about the course instructor. Dikins method matlab files model predictive control matlab files stochastic model predictive control. Bindels lecture notes on regularized linear least squares. Quantitative risk management using robust optimization. Lecture notes on robust optimization, by dimitris bertsimas and dick. Part of the lecture notes in computer science book series lncs, volume 6508. Lecture 08 revisit jensen inequality, convexity preserveing operations lecture 09 conjugate function, quasiconvex functions, logconcave functions, kconvexity lecture 11 optimization application.

Nemirovski, robust optimization, princeton university press. Robust optimization of graph partitioning and critical node detection in analyzing networks. Quantitative risk management using robust optimization lecture notes erick delage september 4, 2019. View notes bdc6218 lecture notes 1 from bdc 6218 at national university of singapore. Notes on relaxation and randomized methods for nonconvex qcqp. Bdc6218 lecture notes 9 robust optimization bdc 6218. In these notes we mostly use the name online optimization rather than online learning, which seems more natural for the protocol described below. We hope to provide the participants, in an online fashion, with selfcontained lecture notes. Berkeley perception, inference, and decision pid group.

We develop a family of convex optimization programs, based on the distributionally robust optimization framework 26, 5, 12, 6, which allow us to provide con. Lectures on robust convex optimization arkadi nemirovski. Brown y, constantine caramanis z july 6, 2007 abstract in this paper we survey the primary research, both theoretical and applied, in the. A robust optimization approach to supply chain management. Lecture notes for statistics 311electrical engineering 377.

In this lecture, we give a brief introduction to robust optimization section 1 robust control section 2. Robust optimization models can be useful in the following situations. View notes bdc6218 lecture notes 9 from bdc 6218 at national university of singapore. The theory part covers basics of convex analysis and convex optimization problems such as linear programing lp, semidefinite programing sdp, second order cone programing socp, and geometric programing gp, as well as duality in general convex and conic optimization problems. Robust optimization of graph partitioning and critical. Fortuitously, a general approach to robust design can be formulated in terms of optimization techniques, further extending the usefulness of these methods. Robust optimization refers to the modeling of optimization problems with data uncertainly. Lecture notes for stat260 robust statistics jacob steinhardt last updated. The optimization of nonlinear functions begins in chapter 2 with a more complete treatment of maximization of unconstrained functions that is covered in calculus. View notes bdc5111 lecture notes 7 from bdc 5111 at national university of singapore.

Theory and applications of robust optimization dimitris bertsimas. G a classified bibliography of research on stochastic pert networks. Assume c is a constant, the robust lp problem is minctx 23. Short course robust optimization and machine learning.

Optimization with uncertain data john duchi notes for ee364b, spring 2015 may 9, 2015 contents 1 robust optimization 1. We typically rst collect training data, then t a model to that data, and nally use the model to make predictions on new test data. Park city mathematics institute, graduate summer school lectures, july 2016. Lectures on robust convex optimization arkadi nemirovski school of industrial and systems engineering. Books, book chapters, and lecture notes introductory lectures on stochastic convex optimization, john c. Motivation and definition of globalized robust counterpart computational tractability prerequisites. Because of our goal to solve problems of the form 1. Bdc6218 lecture notes 1 robust optimization bdc 6218. Berkeley fhl vive center for enhanced reality new journal alert. Online learning is a natural extension of statistical learning. Lecture notes massachusetts institute of technology. Robust optimization bdc 62189 lecture 9 lesson plan robust optimization with recourse robust chance.

Optimization massachusetts institute of technology. Introduction to multidisciplinary system design optimization pdf 1. Optimization of linear functions with linear constraints is the topic of chapter 1, linear programming. Models and techniques for transportation systems 5868 2009, paperback at the best online prices at ebay. A robust design is a design which can tolerate variation. November 25, 2019 lecture 1 1 what is this course about. Basic knowledge of convex analysis and nonlinear optimization.

There are constraints with uncertain parameters that must be satis. When in doubt on the accuracy of these notes, please cross check with the instructors notes, on aaa. This section provides the lecture notes from the course along with the schedule of lecture topics. Nemirovski lectures on robust convex optimization lecture notes, transparencies 8. Robust optimization with uncertain data notes matlab and julia files distributional robustness and chance constraints. Lecture notes and background materials on lebesgue theory from a hilbert and banach space perspective. Introduction to robust optimization schedule lecture. Convex optimization lecture notes for ee 227bt draft, fall.

Eccv workshop on holistic scene structures for 3d vision, glasgow, scotland, august 23, 2020 international conference on learning representations, ethiopia, april 2630, 2020. U if c is also uncertain, the problem can be written as min. Stochastic an introduction to stochastic differential equations lawrence c. Performance analysis in robust optimization springerlink. Lecture notes optimization methods sloan school of. Nemirovski, introduction to linear optimization lecture notes, transparencies 9. This paper considers distributionally robust formulations of a two stage stochastic programming problem with the objective of minimizing a distortion risk of the minimal cost incurred at the second stage.

In this section we learn how to apply optimization methods to determine a robust design. Our focus will be on the computational attractiveness of ro approaches, as well. The course is covered by these lecture notes and more than covered by the book a. We carry out a stability analysis by looking into variations of the ambiguity set under the wasserstein metric, decision spaces at both stages and the support set of the random variables. Optimizationwithuncertaindata john duchi notes for ee364b, spring 2018 may 29, 2018 contents 1 robust optimization 2 1. Some of the problem parameters are estimates and carry estimation risk.