MSIS 22:711:652, Spring 2003 Class meets on Wednesdays 1-3:50pm

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Last changed: 04/21/2003, 11:55:21

    There are no exams or home works or exams for this course

    For each lecture a student volunteer should take charge, take notes from the lectures, prepare a LaTeX document from them and e-mail them to me, so I post them in the web page. See the Notes page for details

    Each student should also give a presentation, either of a research paper or a project he or she is undertaking.

    There are no textbooks assigned for this course. Appropriate texts and papers will be available in the reserves section of the library.

Topics: A. Unconstrained Optimization

    Convex functions (read Bertsekas

    Optimality conditions for optimization over convex and related functions

    The steepest descent method

    Line search along a given direction

    Newton's Method

    Quasi-Newton Methods

    Truncated Newton Methods

Topics: B. Constrained Optimization (nonlinear Programming)

    Cone LP and extension of linear programming to convex programming

    Properties of convex sets: Separation theorems, Farkas Lemma, Caratheodory's Theorem, Helly's Theorem

    Duality theory and complementarity problems

    Linear Programming (LP), Quadratic Programming (QP), Quadratic Cone Programming (QCP), Semidefinite Programming (SDP)

    Lagrangean duality and Karush Kuhn Tucker (KKT) conditions

    Interior Point methods, and Logarithmic barrier functions

    Application of interior point methods for LP, QP, QCP and SDP

    Penalty Methods

    Dual and Lagrangean methods

    Other methods (SQLP, gradient projection, reduced gradient)

References:

  1. Bertsikas, D. "Nonlinear Programming", Athena Scientific, 1995

  2. Fiacco, A. and McCormick, G. "Nonlinear Programming, Sequential Unconstrained Minimization Techniques", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1990

  3. Luenberger, D. "Linear and Nonlinear Programming", Second Edition, Addison-Wesley, 1984

  4. Mangasarian, O. "Nonlinear Programming", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1994