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Global optimization: analytical and simuation-based approach
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Global optimization: analytical and simuation-based approach
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Academic year 2017/2018
- Teacher
- Prof. Paolo Brandimarte (Lecturer)
- Type
- Basic
- Delivery
- Formal authority
- Language
- Italian
- Attendance
- Obligatory
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Sommario del corso
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Course objectives
Extremely efficient algorithms are available for convex optimization problems, but the picture is more complicated for non-convex optimization. Many engineering design problems call for global, rather than local optimization algorithms. Non-convex problems must also be solved in financial models calibration, which is a form of inverse problem, as well as in some statistical estimation problems. Efficient methods may be applied to specific cases featuring some structure (e.g., minimization of a concave function on a convex set), whereas the general problem is quite challenging. In some cases, function evaluation is cheap, and flexible stochastic search procedures may be applied if we just need a good solution. However, in other cases the performance measure to be optimized is estimated by a costly simulation experiment, and we need suitable way to squeeze the most information we can out of each function evaluation. Finally, we might wish to find a provably optimal solution, which may be obtained by branch-and-bound methods. We consider continuous non-convex optimization, but many concepts may be applied to integer programming as well. The aim of the course is to give an overview of these algorithms, using MATLAB as a demonstration tool. Knowledge of basic optimization theory (nonlinear programming) is assumed.
Prerequisites: Some familiarity with standard nonlinear programming concepts (convexity, first-order optimality conditions, Lagrange multipliers, etc.), as well as a working knowledge of MATLAB. We will also use AMPL (www.ampl.com) to build and solve optimization models (a free, time-limited license will be provided).
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Course delivery
Content: Classes of global optimization problems and algorithmsMethods for specific problems (concave optimization, dc programming, etc.)Branch and bound methods for Lipschitzian optimizationStochastic and direct search methods (pattern search, genetic algorithms, particle swarmoptimization)Simulation-based optimization and metamodelingSuggested readings and bibliography
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- Ignacio E. Grossmann (ed.). Global Optimization in Engineering Design. Springer, 1996.J. Pinter. Global Optimization in Action. Continuous and Lipschitz Optimization: Algorithms,Implementations and Applications. Springer 1996.R. Horst, Panos M. Pardalos, Nguyen Van Thoai. Introduction to Global Optimization (2nded.). Springer, 2008.Jack P.C. Kleijnen. Design and Analysis of Simulation Experiments, Springer, 2008Y.D. Sergeyev, D.E. Kvasov. Deterministic Global Optimization: An Introduction to theDiagonal Approach. Springer, 2017.Journal papers will be uploaded on the course web page.
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Note
Assessment In order to formally record the associated credits, individual homework will be assigned during the course, with firm deadlines along the way. You are required to write MATLAB code (possibly, AMPL scripts, too).
Schedule Lectures will be given at Dipartimento di Scienze Matematiche (DISMA), Politecnico di Torino, in Aula Buzano (the internal lecture/seminar room of DISMA, third floor).
Lecture Date
- Wednesday, May 2 nd 10:00 - 13:00
- Wednesday, May 9 th 10:00 - 13:00
- Wednesday, May 16th 10:00 - 13:00
- Wednesday, May 23rd 10:00 - 13:00
- Wednesday, May 30th 10:00 - 13:00
Duration: 15 hours (3 cfu)
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