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

A diagonal matrix and its associated quadratic form

Define a diagonal matrix:

D := mbox{bf diag} (1,4,-3) = left( begin{array}{ccc} 1 & 0 & 0 0 & 4 & 0 0 & 0 & -3 end{array} right).

For the matrix above, the associated quadratic form is

q(x) = x^T left( begin{array}{ccc} 1 & 0 & 0 0 & 4 & 0 0 & 0 &-3 end{array} right) x = x_1^2 + 4x_2^2 - 3 x_3^2.