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"Since the building of the universe is perfect and is created by the wisdom creator, nothing arises in the universe in which one cannot see the sense of some maximum or minimum." (Leonard Euler)

This is an introductory course on linear and nonlinear optimization. It is designed for senior-level undergraduate students (first-year graduate students are also welcome).

Schedule: Tue Thu 11:30-12:50pm, 165 Everitt Lab.

Instructor: Daniel Liberzon
Office: 144 CSL. Email: liberzon at uiuc.edu. Phone: (217) 244-6750. Office hours:

Teaching assistant: Mike Chen
Office: Email: mikechen@uiuc.edu. Phone: Office hours: Wed 4:30-6pm.

Prerequisites: Linear algebra and vector calculus. Basic programming skills.

Textbook: D. Luenberger, Linear and Nonlinear Programming, 2nd edition, 1984 (reprinted in 2003). Available in bookstore.
Supplementary texts: D. Bertsekas, Nonlinear Programming, 2nd edition, 1999. On reserve in Grainger library.
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. Freely available online here.

Grading policy: Bi-weekly homework - 30%, midterm exam - 30%, final exam - 40%.

Course outline:

1. Linear optimization.
Linear programs. Fundamental theorem of linear programming.
Basic concepts of convex analysis. Fundamental theorem and convexity.
Simplex method.
Duality in linear programming. Relations to simplex method.

2. Nonlinear unconstrained optimization.
Basic optimality conditions. Convex optimization.
Gradient and Newton methods.
Line search methods. Convergence analysis of gradient and Newton methods.
Conjugate gradient methods.
Quasi-Newton methods.

3. Nonlinear constrained optimization.
Constraints. Basic optimality conditions. Lagrange multipliers.
Primal gradient methods.
Penalty and barrier functions. Interior-point algorithms.
Duality. Dual and primal-dual methods. Cutting plane methods.
Lagrange methods for quadratic programming.

Other topics (time permitting).