Optimization

3 cr · Graduate

This course, cross-listed with MATH 4490 , introduces the theory and practice of optimization. Topics include unconstrained optimization (quasi-Newton's, BFGS, nonlinear conjugate gradient methods), linear programming (Simplex method, duality), nonlinear constrained optimization (optimality conditions, duality, saddle point theory, barrier and penalty methods, Slater's condition) and integer programming (branch- and-bound, cutting plane and branch-and-cut methods). Applications to calculus of variations, statistics, data science, optimal control, signal processing and neural networks are given. Some computer programming will be required. This course is especially useful for students studying Data Science. Students cannot obtain credit for both MATH 4490 and MATH 7490 .