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Introduction to Optimization Theory and Applications Introduction to Optimization Theory and Applications: Course Overview and Linear Programming Overview WIFI: SSID Student USERname ucsc-guest 1 Password EnrollNow! James G. Shanahan 1Independent Consultant EMAIL: James_DOT_Shanahan_AT_gmail_DOT_com TIM 206 (30155) Introduction to Optimization Theory and Applications Thursday, January 10, 2013 Lecture 01 TIM 206206 (30155 (30155 ) )Introduction Introduction to Optimizationto Optimization Theory Theory and Applications, and Applications, Winter 2013Winter © 2013 James© 2013 G. James Shanahan G. Shanahan 1 Course Info • http://courses.soe.ucsc.edu/courses/tim206 • https://courses.soe.ucsc.edu/courses/tim206/ Winter13/01 – Schedule – Exam during TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 2 Performance Evaluation Final Exam (closed book): Week 11 of the Quarter Performance Evaluation: Homework 30% Midterm 20% (Week 6 of the Quarter) Class participation 20% Final Exam 30% (Week 11 of the Quarter) TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 3 Audience Participation TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 4 Questionnaire • Background – Industry/Academia – Major – Programming experience • Expectations from taking TIM206 TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 5 Brief Bio James G. Shanahan • 25 years in the fields of data mining and operations research – Principal and Founder, Boutique Data Consultancy • Clients include: Adobe, Digg, Adobe, SearchMe, AT&T, SkyGrid, TapJoy – Affiliated with University of California Santa Cruz (UCSC, ISM250,251,209) – Chief Scientist, Turn Inc. (A CPX ad network, DSP) – Principal Scientist, Clairvoyance Corp (CMU spinoff; sister lab to JRC) – Co-founder of Document Souls (an anticipatory information system) – Research Scientist, Xerox Research – Research Engineer, Mitsubishi Group – PhD in machine learning (1998), University of Bristol, UK; B.Sc. Comp. Science (1989), Uni. of Limerick, Ireland • Areas of expertise include: – Local search, web search, online advertising, machine learning, ranking, user modeling, statistics, social networks TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 6 Disclaimer • The Authors retains all rights, including copyrights and distribution rights. • No publication or further distribution in full or in part permitted without explicit written permission from the author • Living vicariously! TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 7 • . TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 8 Click here https://courses.soe.ucsc.edu/courses/tim206/Winter13/01 Course Description • Essentially, every problem in business, computer science and engineering can be formulated as the optimization of some function under some set of constraints. – This universal reduction automatically suggests that such optimization tasks are intractable. Fortunately, most real world problems have special structure, such as convexity, locality, decomposability or submodularity. – These properties allow us to formulate optimization problems that can often be solved efficiently. – As such operations research is a quantitative discipline that deals with the application of advanced analytical methods to help make better decisions. – The terms management science and decision science are sometimes used as more modern-sounding synonyms. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 9 Applications of OR abound! • Techniques from operations research are leveraged within many industries, in both online and offline modes, and are responsible for both batch and real-time decision-making involving trillions of dollars ($10^12) annually worldwide. For example: – Finance: How Wall Street manages stock portfolios? – Digital Advertising: How publishers optimize advertiser revenue online? – Logistics: How Fedex ships billions of packages annually across 220 countries? – Social networks: How to suggest people you may know? – Web search: How to rank web pages with out queries? – Healthcare: How do hospitals run? From organ allocation to schedule generation? Cancer treatment TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 10 Some applications of operations research Other Areas • Digital Advertising • Web search TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 11 Class Topics • More concretely, this class serves as a first graduate course in optimization with an emphasis on theory, intuition, and problem solving in management and engineering. • This class will focus on problem formulation, software technologies and analytical methods for optimization serving as an introduction to a wide variety of optimization problems and techniques including: – linear programming, nonlinear programming, dynamic programming, network flows, integer programming, heuristic approaches, Markov chains, game theory, and decision analysis. TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 12 Lecture Schedule Date Week Lecture Topics 1/10/12 1 Introduction and Linear Programming Intro, intro R part 1 1/17/12 2 Simplex Method and Sensitivity and Duality, intro R part 2 Other LP Methods, LP Applications, Transportation, Assignment and 1/24/12 3 Network Optimization Problems 1/31/12 4 Nonlinear Unconstrained, Gradient descent etc. 2/7/12 5 Nonlinear Constrained, convex optimization, machine learning 2/14/12 6 Exam, (and Dynamic Programming) Integer Programming, Branch and Bound, Multiple choice Knapsack Problem (MCKP), [Genetic Algorithms] Optimal Bid Determination in 2/21/12 7 Sponsored Search as an MCKP 2/28/12 8 Metaheuristics and Markov Chains 3/7/12 9 Game Theory, Decision Analysis and Queueing Theory 3/14/12 10 Inventory Theory and Simulation Wk of 3/18 11 Final Exam: Closed book final Exam will be during this week TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 13 Upon completion one should be able to: • Describe core optimization techniques – e.g., linear programming, nonlinear programming, convex optimization, dynamic programming, genetic algorithms, Markov processes and more – Discuss the pros and cons of these approaches – Explain how to use these approaches and solve problems in the fields of digital advertising and marketing, healthcare, logistics and planning, airline industry, ecommerce • Identify real-world problems that could be solved using optimization techniques • Solve real-world optimization problems in the above fields using solvers, and other optimization software (and possibly implement a couple of the above algorithms from scratch; this is not a requirement though) • Optional: gain a proficiency optimization problem solving in Excel and in R (R is optional but a great skill to develop!). TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 14 TIM 206 Background • This course is introductory and will develop the fundamental operations research models and techniques in the context of real world applications and examples. – We will develop the techniques systematically and sequentially, but will move back-and-forth the different real world applications and domain areas. – The subsequent courses, such as ISM 250 and 251, will expand on the techniques and domain areas such as web mining, computational advertising and online marketing, social networks and relational learning, reinforcement learning, constrained optimization, and also explore significant projects, including possibly with industry. • Prerequisites: Students should have some background in probability, statistics, calculus, and linear algebra, though most of the concepts from these areas, which are core to optimization, will be reviewed for completeness during the course. TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 15 TIM 206 is timely! • TIM 206 (Survey class) – Precursor to TIM 250 (Stochastic optimization) which goes deeper into NLP, MDPs, Convex optimization, Machine learning as optimization) and TIM 251 (scalable, distributed decision support systems) • …. with applications in digital advertising and online marketing, healthcare, airlines, financial • Timely: – Growing flood of online data, Budding industries (e.g., digital advertising, healthcare, financial) – Computational power is available (PC, Cloud computing, Hadoop) – Progress in algorithms and theory and applications TIM 206 (30155 ) Introduction to Optimization Theory and Applications, Winter 2013 © 2013 James G. Shanahan 16 Summaries à Decisions à Personalization • The old days were about asking, ‘What is the biggest, smallest, and average?’ ” says Michael Olson, CEO of startup Cloudera. “Today it’s, ‘What do you like? Who do you know?’ It’s answering these complex
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