Math 516A
Numerical Optimization

James Burke

Spring 2005, Tuesday/Thursday 8:30-9:50
The course will focus on the design and the analysis of numerical algorithms for solving continuous optimization problems with a finite number of variables. Algorithms include methods for unconstrained differentiable minimization (steepest descent, Newton method, conjugate gradient, quasi-Newton, Nelder Mead simplex), methods for differentiable minimization with convex constraints (Frank-Wolfe, gradient projection, manifold minimization), methods for differentiable minimization with nonconvex constraints (penalty, multiplier, sequential quadratic programming), interior point method, and subgradient method. Issues such as algorithm design, implementation, robustness and efficiency (convergence, convergence rate, complexity), and solution quality will be studied. Some programming in Matlab will be involved.

Textbook: Nonlinear Programming, 2nd edition, 1999, by Dimitri Bertsekas, Athena Scientific Publishing, Belmont, MA.

Prerequisite: MATH 515.