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

* multivariate calculus and linear algebra

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.

* 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)

* 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]

* Semi-definite programming 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]

* 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

* 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