NetSys 254 Nonlinear Optimization Methods (3) [cross-listed with EECS 261B]. Formulation, solution, and analysis of nonlinear programming problems. Unconstrained optimization, optimization over a convex set, Lagrange multiplier theory, Lagrange multiplier algorithms, duality theory, convex programming, dual methods, and multi-objective optimization theory. Emphasizes mathematical analysis. Prerequisite: Mathematics 2J or consent of instructor.

• Unconstrained optimization: gradient methods, convergence, and efficiency
• Newton methods, conjugate directions, quasi-Newton methods, convergence, and efficiency
• Convexity: convex sets, functions, optimization, quadratic and geometric programming
• Lagrange multiplier theory: equality and inequality constrained optimization
• Lagrange multiplier issues: sensitivity analysis, pricing, KKT and Fritz-John conditions
• Lagrange multiplier algorithms: penalty methods, sequential quadratic programming (SQP)
• Duality: weak and strong duality, Fenchel duality, complimentarity
• Applications: approximation, fitting, and statistical estimation
• Advance topics: Cutting plane methods and subgradients