Introduction to Optimization

Prerequisite: Admission to the MS program in Mathematics or consent of instructor This course introduces the fundamental problems of nonlinear constrained and unconstrained optimization. In particular, the topics covered include optimization without calculus using Arithmetic Mean-Geometric, Holder and Minkowski, and Cauchy's inequalities. The nonlinear unconstrained optimization methods including One-Dimensional Search Methods, Gradient methods, Newton's method and Conjugate Direction methods are also examined. The nonlinear constrained optimization methods including convex optimization problem is focused. Numerical algorithms for constrained optimization such as Projected Gradient method with linear constraints, Lagrangian algorithms and Penalty Function methods are discussed. Offered alternate years.