 Aims
Introduce a modern theory of optimization and general principles of complexity analysis of algorithms for solving nonlinear problems. Present the most efficient algorithmic schemes.
Main themes
General nonlinear optimization. Smooth and non-smooth convex optimization. Interior-point methods. Prerequisites: standard undergraduate level in Linear Algebra and Calculus.
Content and teaching methods
-General problem of nonlinear optimization. Black-box concept. Iterative methods and analytical complexity. Gradient method and Newton method. Local complexity analysis.
-Convex optimization: convex sets and functions; minimization of differentiable and non-differentiable convex functions; lower complexity bounds; optimal methods.
-Interior-point methods: notion of self-concordant functions and barriers; path-following methods; structural optimization.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
- copy of transparencies and of the text of the lectures.
- Yu.Nesterov. "Introductory lectures on convex optimization. Basic course." Kluwer 2003
- P. Polyak, « Introduction in optimization », J. Willey & Sons, 1989
- Yu. Nesterov, A. Nemirovsky, « Interior-point polynomial algorithms in nonlinear optimization », SIAM, Philadelphia, 1994.
The course is given in English.
Evaluation: a written exam (in French or in English).
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INFO22
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(4 credits)
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MAP22
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Deuxième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(4 credits)
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MAP23
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Troisième année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(4 credits)
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MATH22/G
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Deuxième licence en sciences mathématiques
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(4 credits)
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