Mth 564 Numerical Optimization I

Fundamentals of unconstrained optimization, necessary and sufficient conditions, overview of numerical algorithms, rate of convergence, line search and trust-region methods. Gradient descent, conjugate gradient, Newton and quasi-Newton methods, nonlinear least-squares problems, Gauss-Newton and Levenberg-Marquardt methods, practical applications. This is the first course in a sequence of two: Mth 564 and Mth 565. Expected preparation: knowledge of a high-level programming language such as MATLAB, Python, R, or C/C++.