Convex Optimization

When I attended this course, I found myself spending most of time on reading the book written by Stephen Boyd. This book really impressed me a lot and I bought it for my first English paper book.

I think the charm of Convex Optimization lies in: the locally optimal solution will be the globally optimal one if the problem can be constructed as a convex one.

Syllabus

Convex Sets

• Affine and convex sets
• Operations that preserve convexity
• Generalized inequalities
• Supporting hyperplanes
• Dual cones

Convex Functions

• Basic Properties
• Operations that preserve convexity
• Quasiconvex Functions
• The Conjugate Functions
• Log-concave and log-convex functions

Duality Theory

• The Lagrange dual function
• Saddle-point
• Sensitivity Analysis

Optimization Methods

• Gradient-based methods
• Simplex Algorithm for Linear Programming
• Interior-Point Method

Study Note

{x|ax=b}

Two interpretations for it:

• it is a solution set for the linear equation
• a hyperplane with normal vector a and the constant b determines the offset of the hyperplane from the origin, if we change it into the form: {x|a(x-x0)=0}