Reading Group on Optimization Theory

Textbook: D.P.Bertsekas, Nonlinear Optimization, Athena Scientific with online notes

References:

· Bazaraa, Nonlinear Programming: Theory and Algorithm, 2^nd Edition, John Wiley & Sons, 1993

· S.Zlobec, Stable Parametric Programming, Kluwer Academic Publishers, 2001

· Ben-Israel, A.Ben-Tal, S. Zlobec, Optimality in Nonlinear Programming: A Feasible Directions Approach, Wiley, 1981

· Mangasarian, Nonlinear Programming, SIAM Classics, 1969

· D. Bertsekas, Convex Analysis and Optimization, Athena Scientific.

Computing Software:

· CVX: Matlab Software for Disciplined Convex Programming

Related Course Web Pages:

· EE364: Convex Optimization by S. Boyd, Stanford

· CDS 270: Optimization, Game and Layering in Communication, Caltech

· Nonlinear Programming, MIT OCW, 2004

· Nonlinear Programming, MIT OCW, 2003

· Convex Optimization, University of Toronto, 2006

· Auctions Reading Group, University of California, Berkeley

Time: Thursdays 5:30pm-7:00pm and Saturdays 1:00pm-3:00pm

Papers:

On Application of Duality and Network Resource Allocation

[1]. Optimization Flow Control, I: Basic Algorithm and Convergence, S. H. Low and D. E. Lapsley, IEEE/ACM Transactions on Networking, 7(6):861-75, December 1999.

[2]. Rate control in communication networks: shadow prices, proportional fairness and stability, F. P. Kelly, A.K. Maulloo and D. K. H. Tan, Journal of the Operational Research Society 49 (1998), 237-252.

On Game Theory

[3]. How bad is selfish routing?, T. Roughgarden and E. Tardos,Journal of the ACM, 2002.

[4]. More to be added

Weekly Schedule:

TIME	Material	Comments
January 25, 2007	Newton’s Method in Unconstrained Optimization Problem, Chapter 1, BER	Notes, Supplement on Matrices
February 1, 2007	Lagrange’s Necessary Condition from Penalty and Elimination Approaches, Chapter 3, BER	Notes, Summary
February 3, 2007	Projection Theorem, Chapter 2, BER	Notes, Summary
February 8, 2007	Lagrange’s Sufficient Conditions and Sensitivity Analysis	Notes, Summary
February 11, 2007	TBA	Notes, Summary
	KKT and Fritz-John Optimality Conditions, Chapter 3, BER	Notes, Summary
	TBA	Notes, Summary
	Linear Constraints and Duality, Chapter 3, BER	Notes, Summary
	TBA	Notes, Summary
	Duality Theory I, Chapter 5,BER	Notes, Summary
	TBA	Notes, Summary
	Duality Theory II, Chapter 5,BER	Notes, Summary
	TBA	Notes, Summary
	Duality Theory III, Chapter 5,BER	Notes, Summary
	TBA	Notes, Summary
	Duality Theory IV, Chapter 5,BER	Notes, Summary
	TBA	Notes, Summary