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Optimization under uncertainty: modeling and solution methods
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Optimization under uncertainty: modeling and solution methods
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Academic year 2014/2015
- Teacher
- Prof. Paolo Brandimarte (Lecturer)
- Type
- A scelta dello studente
- Course disciplinary sector (SSD)
- ING-IND/35 - ingegneria economico-gestionale
MAT/09 - ricerca operativa - Delivery
- Tradizionale
- Language
- Inglese
- Prerequisites
- Some familiarity with standard linear programming models; essentials of probability theory.
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Sommario del corso
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Course objectives
The aim of the course is to strengthen the knowledge of optimization methods, extending modeling and solution procedures to cases affected by significant uncertainty. Uncertainty is pervasive in many branches of engineering and social sciences, including finance, supply chain management, energy markets, and telecommunication networks. Emphasis is on stochastic programming models, but, since a stochastic characterization of uncertainty is not always available, reliable, or appropriate, we will also consider robust optimization frameworks. Furthermore, since solving multistage stochastic optimization models is quite challenging, we will also deal with approximate dynamic programming methods that, among other things, illustrate the connection between mathematical optimization and machine learning. Case studies and examples are used throughout the course to illustrate the relevance of its content.- Oggetto:
Program
Introductory examples and motivations; the impact of uncertainty; expected value of perfect information and value of the stochastic solution.Alternative paradigms: stochastic programming with recourse; chance-constrained optimization; robust optimization.A refresher on optimization theory: convexity; duality; solution methods for linear, nonlinear, and mixed-integer programming models.Decomposition methods for stochastic programming models with recourse.Solution methods for mixed-integer stochastic optimization models.The formulation of dynamic optimization models under uncertainty.Scenario generation: Monte Carlo sampling; deterministic methods (quasi-Monte Carlo, Gaussian quadrature, moment matching).Risk measurement and management: utility functions; coherent risk measures.Simulation-based optimization.Dynamic programming: Bellman's equation; learning the value function by Monte Carlo simulation and linear regression.Robust optimization: nonstochastic representation of uncertainty; solution methods based on convex optimization.Suggested readings and bibliography
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- P. Brandimarte. Quantitative Methods: An Introduction for Business Management. Wiley 2011.P. Brandimarte. Handbook in Monte Carlo Methods: Applications in Financial Engineering, RiskManagement, and Economics. Wiley 2014.A.J. King, S.W. Wallace. Modeling with Stochastic Programming. Springer, 2012.W.B. Powell. Approximate Dynamic Programming: Solving the Curses of Dimensionality (2nded.). Wiley, 2011.A. Ben-Tal, L.. El Ghaoui, A, Nemirovski. Robust Optimization. Princeton University Press, 2009.S.W. Wallace, W.T. Ziemba (eds.). Applications of Stochastic Programming. SIAM, 2005.
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Note
ASSESSMENTPlease note that, unlike previous editions of the course, in order to formally record the associated credits (6), passing a written exam is required. We will arrange two dates, one before and one after summer. The exam is closed book, but not quite challenging, as its aim is just to provide PhD students with some incentive to actively follow the course and get acquainted with its content.SCHEDULELectures will be given at Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, in Aula Buzano (the internal lecture/seminar room of DISMA, third floor).Friday, April 10th 9:30 - 12:30Monday, April 13th 9:30 - 12:30Tuesday, April 21st 9:30 - 12:30Monday, April 27th 9:30 - 12:30Monday, May 4th 9:30 - 12:30Monday, May 11th 9:30 - 12:30Monday, May 18th 9:30 - 12:30Friday, May 22nd 9:30 - 12:30Monday, May 25th 9:30 - 12:30Friday, May 29th 9:30 - 12:30- Oggetto:
