• 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.

• Convex Optimization by Stephen Boyd and Lieven Vandenberghe, available online
• Convex Analysis Rockafellar (suppl reference)

• Introduction

• 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]

* 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