Spring Semester 2011

Class meetings: Tues, 5:10-7:00pm, in CIWW 312.

Last day of class: Tuesday, May 3.

Final project due: Wednesday, May 11.

HW2, due March 8, 2011

HW3, due March 22, 2011

HW4, due April 12, 2011

Homeworks may be submitted in written form or via email. They must be in the instructor's possession by 5pm on the due date. Without explicit permission from the instructor in advance, late homework will be marked down by 30% for every day of lateness.

January 25. |
Course overview. Linear programming. Chapter 13 of textbook. |

February 1. |
Feasible descent directions. Optimality conditions. Farkas' Lemma. |

February 8. |
Simplex method for all-inequality form. First homework assignment (HW1), due February 15. |

February 15. |
Simplex method for all-inequality form. Linear algebra issues; updating the LU factors. |

February 22. |
Simplex method for standard form. Duality. Second homework assignment (HW2), due March 8. |

March 1. |
Systems of nonlinear equations. Newton's method. Chapter 11 of textbook. Interior methods for LP. Chapter 14 of textbook. |

March 8. |
Short revisit of Newton's method for nonlinear equations
and primal-dual interior LP methods. Introduction to unconstrained optimization. Chapters 2 and 3 of textbook. Third homework assignment (HW3), due March 22. List of possible projects handed out. |

March 15. |
No class (spring break). |

March 22. |
Local models in unconstrained optimization. Introduction to line search and trust region methods. Choosing the step length. Backtracking. The Wolfe conditions. Steepest descent. |

March 29. |
Steepest descent and its rate of convergence. Newton's method for unconstrained optimization. Modified Newton methods based on eigensystem, Cholesky, and symmetric indefinite factorizations. Fourth homework assignment (HW4), due April 12. Chapters 3,4, and 6 of textbook. |

April 5. |
Quasi-Newton methods. Implementation of quasi-Newton methods. Gradient-related search directions. Convergence of line search methods. Chapter 8 of textbook. |

April 12. |
Equality-constrained quadratic programming. KKT systems. Introduction to inequality-constrained quadratic programming. |

April 19. |
Active-set methods for inequality-constrained quadratic programming. Linearly constrained optimization of a nonlinear function. Introduction to nonlinear equality constraints. Chapter 12 of textbook. |