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 squared linear function

A squared linear function is a quadratic function q : mathbf{R}^n rightarrow mathbf{R} of the form

q(x) = (v^Tx)^2,

for some vector v in mathbf{R}^n.

The function vanishes on the space orthogonal to v, which is the hyperplane defined by the single linear equation v^Tx = 0. Thus, in effect this function is really one-dimensional: it varies only along the direction v.

Level curve of $p$ 

Level sets and graph of a dyadic quadratic function, corresponding to the vector v = (2,1). The function is constant along hyperplanes orthogonal to v.