==== Convex Optimization ====

== Course information ==
  * Instructor: Xiaohui Xie
  * Meeting information: TT 3:30-4:50pm    Room: ICS 180
  * Office hours: TT after class

== Prerequisites ==

  * multivariate calculus and linear algebra

== Course Description ==

This course will focus on formulating and solving convex optimization problems arising in engineering and science. Topics include: convex analysis, linear and quadratic programming, semidefinite programming, optimality conditions, duality theory, interior-point methods, subgradient methods, convex relaxation.

== Textbook ==
  * [[http://www.stanford.edu/boyd/cvxbook/bv_cvxbook.pdf|Convex Optimization]] by Stephen Boyd and Lieven Vandenberghe, available online
  * [[http://www.amazon.com/Analysis-Princeton-Mathematical-Tyrrell-Rockafellar/dp/0691080690|Convex Analysis]] Rockafellar (suppl reference)

== Lectures ==
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/introduction.pdf|Introduction]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_sets.pdf|Convex Sets]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/convex_functions.pdf | Convex Functions]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimization_problems.pdf | Optimization Problems]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/optimality_conditions.pdf | Optimality Conditions]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/duality.pdf | Duality]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/unconstrained_opt.pdf | Unconstrained minimization]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/equality.pdf | Equality constrained minimization]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/interior.pdf | Interior-point methods]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/sdpintro.pdf | Introduction to Semidefinite Programming (SDP)]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/semidef_prog.pdf | SDP]]

Modeling and application
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods.pdf | Stochastic subgradient methods]]
    * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/stochastic_subgradient_methods_report.pdf | more details]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning.pdf|Multitask feature learning]]
    * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Multitask_Feature_Learning_report.pdf | More details]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/FengJiang.pdf | Beamforming Optimization of MIMO Interference Network]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/color_constancy.pdf | Color Constancy]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/approximation.pdf | Approximation and fitting]] 
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/struct_var_detection.pdf | Detecting genetic variation using fused Lasso]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf | Load balancing on a heterogeneous cluster]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/graph_isomorphism.pdf | Detecting graph isomorphism]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Load_balancing_ConvOpt.pdf | Load balancing on a heterogeneous cluster]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/Modeling_Marketing_Promotion_Choices.pdf |  Modeling marketing promotion choices]]
  * [[http://www.ics.uci.edu/~xhx/courses/ConvexOpt/projects/PatrickFlynn.pdf | Conjugate gradient method]]


== Key dates ==
  * Final exam: Mar 15, 4:00-6:00pm  (Bring one examination blue book!) 
  * Final project due: Mar 18, 5pm, hard copy in Bren Hall 4058

== Exercise ==
  * Convex sets: 2.1, 2.9, 2.12, 2.15, 2.23, 2.24, 2.33  (from the textbook)
  * Convex functions: 3.2, 3.15, 3.16, 3.36, 3.42
  * Convex problems; 4.1, 4.65
  * Duality:  5.1, 5.13, 5.38, 5.42