Math 516A
Numerical Optimization
Paul Tseng
Spring 2005, Tuesday/Thursday 8:30-9:50
Ever wondered how optimization problems are solved in real life? This
course will give an overview of numerical algorithms for solving diverse
optimization problems in finite-dimensional space. 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: AMATH/MATH 515.