Optimization Models
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1. Introduction
1.1. Overview
1.2. Optimization Models
2. Linear Algebra
2.1. Vectors
2.2. Matrices
2.3. Linear Equations
2.4.  Least-Squares
2.5. Eigenvalues
2.6  Singular Values
3. Convex Models
3.1. Convexity
3.2. LP and QP
3.3. SOCP
3.4. Robust LP
3.5. GP
3.6. SDP
3.7. Non-Convex Models
4. Duality
4.1. Weak Duality
4.2. Strong Duality
4.3.  Applications
5. Case Studies
5.1. Senate Voting
5.2. Antenna Arrays
5.3. Localization
5.4. Circuit Design

Example of a map

The map f : mathbf{R}^3 rightarrow mathbf{R}^2 with values

f(x) = left( begin{array}{c} sqrt{x_1^2+x_2^2}cos(x_3) sqrt{x_1^2+x_2^2} sin(x_3) end{array}right)

has components the functions f_i : mathbf{R}^2 rightarrow mathbf{R}, i=1,2, with values

f_1(x) = sqrt{x_1^2+x_2^2}cos(x_3), ;; f_2(x) = sqrt{x_1^2+x_2^2}sin(x_3) .