OA4201 Nonlinear Programming.

(Same as MA4301.) Convex sets, convex functions, and conditions for local and global optimality. Elements and convergence of algorithms for solving constrained and unconstrained optimization problems. Introduction to algebraic modeling languages. Many applications of integer and nonlinear programming to military and civilian problems, such as weapons assignments, force structuring, parameter estimation for nonlinear or constrained regression, personnel assignment and resource allocation.

Prerequisite

OA3201

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

• Become familiar with nonlinear optimization models, i.e., mathematical models for decision making in the absence of linear relations between decisions and effects. Learn how to identify different types of models. Study specific models in search & detection, machine learning, statistics, and decision making under uncertainty.
• Become familiar with Pyomo and various open-source solvers for implementation and solution of optimization models. Learn to interpret and validate output from Pyomo.
• Become familiar with elementary convexity theory, i.e., convex sets, convex functions, convex optimization problems, implications for solvability of optimization problems. Learn rules for identifying convex sets and functions.
• Become familiar with basic algorithmic ideas for unconstrained and constrained optimization. Learn how to carry out iterations of gradient descent method, Newton’s method, Armijo step size rule, proximal gradient descent, interior-point method, and subgradient method.
• Develop mathematical reading and comprehension skills. Understand function notation. Learn to read technical literature in Operations Research. Learn to read, understand, and apply definitions and concepts given in mathematical notation.