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Optimization methods are numerical tools inside many engineering software, in industry (aeronautics,…) or services (finance, decision making tools,…). This course is an introduction to the bases of mathematics and algorithmics of continuous optimization. The goal is to get familiar with these notions by manipulating basic mathematical results and some software. We insist on examples, many of them coming from real-life applications.
Contact Jérome MALICK1. Introduction, classification, first examples in finance and weather forcasting. Special classes : quadratic programming, conic progamming, illustrations
2. Theoretical results : convexity, compactness, optimality conditions, KKT theorems.
3. Algorithms for smooth unconstrained optimization : descent methods, line-search, Newton and quasi-Newton methods.
4. Algorithms for nonsmooth optimization : Lagrangian duality, bundle methods, illustration with the electricity production management.
5. Algorithms for smooth constrained optimization : penalization (interior or exterior), SQP methods.
Applied Analysis, Linear Algebra, Numerical Analysis
Written exam + bonus points with homework
N1 = E1 (+ CC)
N2 = E2 (+ CC)
S. BOYD and L. VANDENBERGHE : Convex Optimization, Cambridge, 2004
G. CORNUEJOLS and R. TUTUNCU : Optimization methods in Finance, Cambridge, 2007
J.B. HIRRIART-URRUTY and C. LEMARECHAL : Convex Analysis and Minimization Algorithms (vol. 1 et 2), Springer, 1996
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