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Informatique et Mathématiques appliquées
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> Formation > Cursus ingénieur

Numerical optimization - 4MMON6

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  • Number of hours

    • Lectures : 16.5
    • Tutorials : 9.0
    • Laboratory works : 7.5
    ECTS : 3.0

Goals

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 MALICK

Content

1. 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.



Prerequisites

Applied Analysis, Linear Algebra, Numerical Analysis

Tests

Written exam + bonus points with homework



N1 = E1 (+ CC)
N2 = E2 (+ CC)

Additional Information

Curriculum->Financial Engineering->Semester 8
Curriculum->Math. Modelling, Image & Simulation->Semester 8

Bibliography

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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Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes