

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 email 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 OptimizationConvex 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 QuasiNewton 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:


