• 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
• Convex Functions
• Optimization Problems
• Optimality Conditions
• Duality
• Unconstrained minimization
• Equality constrained minimization
• Interior-point methods
• Introduction to Semidefinite Programming (SDP)
• SDP

Modeling and application

• Stochastic subgradient methods
  • more details
• Multitask feature learning
  • More details
• Beamforming Optimization of MIMO Interference Network
• Color Constancy
• Approximation and fitting
• Detecting genetic variation using fused Lasso
• Load balancing on a heterogeneous cluster
• Detecting graph isomorphism
• Load balancing on a heterogeneous cluster
• Modeling marketing promotion choices
• 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