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, we 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 Deviation variables
- 1.5 Using arrays
- 1.6 Integer exchange method
- 1.7 Simplex method
- 1.8 Examples
- 1.9 Remarks
- 1.10 The case of bounded variables
- 1.11 The 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.