Solving Optimization Problems using the Matlab Optimization
Toolbox - a Tutorial
TU-Ilmenau, Fakultät für Mathematik und Naturwissenschaften
Dr. Abebe Geletu
December 13, 2007
Contents
1 Introduction to Mathematical Programming
1.1 A general Mathematical Programming Problem . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Some Classes of Optimization Problems . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Functions of the Matlab Optimization Toolbox . . . . . . . . . . . . . . . . . . .
2 Linear Programming Problems
2.1 Linear programming with MATLAB . . . . . . . .
2.2 The Interior Point Method for LP . . . . . . . . .
2.3 Using linprog to solve LP’s . . . . . . . . . . . . .
2.3.1 Formal problems . . . . . . . . . . . . . .
2.3.2 Approximation of discrete Data by a Curve
3 Quadratic programming Problems
3.1 Algorithms Implemented under quadprog.m . .
3.1.1 Active Set-Method . . . . . . . . . . . .
3.1.2 The Interior Reflective Method . . . . .
3.2 Using quadprog to Solve QP Problems . . . . .
3.2.1 Theoretical Problems . . . . . . . . . . .
3.2.2 Production model - profit maximization
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4 Unconstrained nonlinear programming
4.1 Theory, optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Problems, assumptions, definitions . . . . . . . . . . . . . . . . . . .
4.2 Optimality conditions for smooth unconstrained problems . . . . . . . . . ....