CES7AC Optimisation
| ECTS Credits: 4 Duration: 36 hours | Semester: S8 | ||
Person(s) in charge: Yannick PRIVAT, Chargé de Recherche UPMC, yannick.privat@upmc.fr | ||||
Keywords: Optimization | ||||
Prerequisites: Linear algebra, differential calculus. Knowledge in linear numerical analysis would be a plus.
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Goal: provide with a basic knowledge allowing, given a practical problem, to choose the adapted algoritms | ||||
Program and contents: Objectives
Analysis (well-posedness of the problem). First and second order optimality conditions, use of convexity. General classes of algorithms: steepest descent, conjugate gradient, quasi-Newton methods. Line search algorithms for choosing an adequate step-length. Global convergence and asymptotic convergence of the algorithms.
Analysis (well-posedness of the problem), optimality conditions. Equality or inequality constraints. Feasible directions. Lagrange and Kuhn and Tucker theorems. Convex problems. Gradient projection and penalty methods. Lagrange-Newton method. The Lagrangian, saddle points and duality. Uzawa method and extensions.
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Abilities: | ||||
Levels | Description and operational vocabulary | |||
Know |
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Understand | ||||
Apply | ||||
Analyze | ||||
Summarize | ||||
Evaluate | ||||
Evaluation: | ||||
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