Nonlinear Optimization (18799
IST-CMU PhD Course
Instructor: João Xavier
jxavier (@) isr.ist.utl.pt
TA: Dragana Bajovic
dbajovic (@) andrew.cmu.edu
The past year's exams are going to be sent soon by email. If you have not received them by Wednesday, April 18, please let the TA know
Homework 5 is available here. It is due April, 4.
Homework 4 is available here. It is due March, 21.
There will be no classes next week, i.e., March 12 and 14 (CMU Spring break). We resume March 19.
Homework 3 is available here. It is due March, 7.
The annotated slides are available here.
Homework 2 is available here. It is due February, 22.
Class cancellation: there is no class on Wednesday, Feb 1.
Office hours for Lisbon students:
with João Xavier: Wednesdays 15h00-16h00 (Lisbon time)
with Dragana Bajovic: Wednesdays 12h00-13h00 (Lisbon time)
Office hours for CMU students (use skype account nonlinear.optimization.18799):
with João Xavier: Wednesdays 16h00-17h00 (Lisbon time) = 11h00-12h00 (Pittsburgh time)
with Dragana Bajovic: Fridays 17h00-18h00 (Lisbon time) = 12h00-13h00 (Pittsburgh time)
Homework 1 is available here. It is due the 8th of February.
A file with the essential background is here
The lectures start January 18, 2012. The schedule is: Mondays and Wednesdays 18h30-20h00 Lisbon time (13h30-17h00 Pittsburgh time). The classroom at CMU is on the INI building, Henry Street. The classroom at IST campus is the CMU Videoconference Room at Pavilhão de Engenharia Civil
Part I: formulation of optimization problems. Convex sets and functions. Recognizing canonical classes of convex programs: linear, quadratic, posynomial, geometric, second-order cone, semidefinite positive. Usage of software packages. Applications in communications, estimation, approximation, control, pattern recognition, graphs, networks, etc.
Part II: conditions for optimality and duality theory. The Karush-Kuhn-Tucker (KKT) conditions for optimality. Geometrical interpretation of KKT conditions. Dual programs, the duality gap and its geometrical interpretation. Applications of duality: provable lower bounds, problem simplification, problem decomposition, convex relaxations of combinatorial problems (e.g. MAXCUT).
Part III: algorithms. Line-search based algorithms for unconstrained optimization: gradient,quasi-Newton BFGS,Newton. Convergence theory and convergence rates. Algorithms for constrained optimization. Interior point algorithms for convex programs. Penalty, barrier, augmented Lagrangian and SQP methods for general (nonconvex) programs.
Part IV: special topics. Nonsmooth optimization and optimization over manifolds.
Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press
Numerical Optimization, J. Nocedal and S. Wright, Springer Series in Operations Research
Lectures on Modern Convex Optimization, A. Ben-Tal and A. Nemirovski, MPS-SIAM Series on Optimization
Nonlinear Programming, D. Bertsekas, Athena Scientific
50% (7 homeworks), final exam 40% (24h take home) , oral examination