•     Required text: Nonlinear Programming, (2nd edition), by D. Bertsekas
•     Required software: Maple  (available in many Rutgers sites)
•     Prerequisites: Advanced calculus, linear programming and/or instructor's consent
•     Course webpage:   ftp://rutcor.rutgers.edu/pub/bisrael/611.html
•     Time: Wednesday, 6:00-9:00 pm
•     Place: Room 139, RUTCOR Building, Busch Campus
•     Instructor: Adi Ben-Israel
•     E-mail: bisrael@rutcor.rutgers.edu
•     Office: 113 RUTCOR Building, Busch Campus
•     Telephone: 732-445-5631
•     Office hours: W 9:00 pm,  and by appointment

This is an introductory doctoral-level course, devoted to the minimization or maximization of a real-valued objective function of several variables, subject to constraints. Both objective and constraints may be nonlinear. The principal topics are

• necessary and sufficient conditions for a point to be a local optimum, and
• iterative algorithms for approximating such points.

All "sections" and "chapters" are from the Bertsekas text.

• Week 1: Overview, unconstrained problems, global/local optima, convex sets and functions, optimality conditions, stationary points. Read: section 1.1 and portions of the appendices.

• Weeks 2-3: Gradient methods: motivation and convergence analysis. Armijo stepsize selection. Linear, sublinear, and superlinear convergence. Gradient relatedness and the capture theorem. Read: sections 1.2-1.3.

• Week 4: Newton methods and their convergence. Survey of other unconstrained methods, including conjugate gradient. Read: section 1.4.

• Weeks 5-6: Optimization over an abstract set. Normal cones, feasible directions and optimality conditions. Variational inequalities. Frank-Wolfe methods and their convergence. Gradient projection methods. Read: chapter 2.

• Weeks 7-8: Problems with functional constraints. Lagrange multipliers and Kuhn-Tucker conditions. Lagrangian functions. Duality for problems with linear constraints. Read: chapter 3 plus handed-out lecture notes.

• Weeks 9-10: Barrier methods. Penalty methods. Read: chapter 4 plus handed-out journal articles.

• Weeks 11-12: Weak and strong duality for nonlinear problems. Convex duality. Read: sections 5.1-5.3.

• Weeks 13-14: Direct Lagrangian methods. Proximal minimization algorithms. Augmented Lagrangian methods and duality.

Workload and grading

There will be approximately eight homework assignments due at regular intervals, all including some
Maple work as well as mathematical exercises or short proofs. The final exam is a take-home exam.
The course grade gives equal weights to the final exam and the homework assignments.