Math 516A
Numerical Optimization
Paul Tseng
Spring 2004, 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.