Optimization

Objectives: Introduction to optimization methods. Context - Problem : In all scientific or economic fields, we are often called upon to optimize a certain criterion, a real function of several real variables, these variables being subject to certain constraints of equalities or inequalities, linear or non-linear. For example, you may want to maximize a profit, or minimize a cost, maximize numerical precision, or minimize spurious noise. Tools: Examples of the use of various software packages (Matlab, Scilab, Maple, Mathematica, Excel).

Matrix analysis, partial derivatives.

* Chapter 1: Linear Optimization - 1.1 Introduction - 1.2 Example - 1.3 Linear optimization problems - 1.4 Variable deviations - 1.5 Use of arrays - 1.6 Integer exchange method - 1.7 Simplex method - 1.8 Examples - 1.9 Remarks - 1.10 Case of bounded variables - 1.11 Case of integer variables - 1.12 Duality * Chapter 2: Nonlinear Optimization - 2.1 Introduction - 2.2 Necessary conditions for a minimum - 2.3 Sufficient conditions for a minimum - 2.4 Quadratic criterion without constraints - 2.5 Case of equality constraints, Lagrange criterion - 2.6 Quadratic criterion with linear equality constraints - 2.7 Quadratic optimization with linear equality constraints - 2.8 Case of inequality constraints - 2.9 Quadratic optimization with linear inequality constraints

Automatic

Course handout. Recommended books: Linear programming with 65 problems modeled and solved, C.Guéret, C.Prins, M.Sevaux, Eyrolles, 2000.