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Matlab Optimization Toolbox

Matlab Optimization Toolbox. By YANG, Haiqin. Outline. Mathematical Programming Linear Programming Quadratic Programming Unconstrained Non-linear Programming. Mathematical Programming. Framework Linear Programming Applications Network flow Transporation. Quadratic Programming

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Matlab Optimization Toolbox

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  1. Matlab Optimization Toolbox By YANG, Haiqin

  2. Outline • Mathematical Programming • Linear Programming • Quadratic Programming • Unconstrained Non-linear Programming

  3. Mathematical Programming • Framework • Linear Programming • Applications • Network flow • Transporation • Quadratic Programming • Applications • Least square approximation • Portfolio optimization

  4. Mathematical Programming • Non-linear Programming • Semi-indefinite Programming

  5. Mathematical Programming • Multiple-Objective Optimization • Applications • Financial applications: maximize return, minimize risk • etc.

  6. Minimization Algorithm

  7. Minimization Algorithm (Cont.)

  8. Equation Solving Algorithms

  9. Least-Squares Algorithms

  10. LP • Formulation • Calling

  11. Implementation of LP • Algorithms • Simplex: medium-scale • Active set: medium-scale • Primal-dual interior point: large-scale • LP standard form • Primal • Dual

  12. Optimal Condition • Karush-Kuhn-Tucker (KKT) condition Complemetarity conditions

  13. Interior Point for LP • Central path

  14. Algorithm

  15. QP • Formulation • Calling

  16. Implementation of QP • Algorithms • Medium-scale: active set • Large-scale: an interior reflective Newton method coupled with a trust region method.

  17. Active Set Method • Transformation • Optimal condition

  18. Unconstrained Non-linear Programming • Formulation • Calling

  19. Implementation Ideas • Formulation • A general descent algorithm

  20. Quasi-Newton Algorithm • Idea • The BFGS - update (Broyde-Fletcher-Goldfarb-Shanon) • The inverse DFP - update (Davidon-Fletcher-Powell)

  21. Line Search • Find step-length • Wolfe conditions • Goldstein conditions

  22. Trust Region Method • Formulation • Algorithm

  23. Other Toolboxes • CVX • http://cvxr.com/cvx/ • Mosek • http://www.mosek.com/ • Yalmip • http://users.isy.liu.se/johanl/yalmip/

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