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

SOCPs include LPs as Special Case

The linear program (LP)

min_x : c^Tx ~:~ a_i^Tx le b_i, ;; i=1,ldots,m,

can be cast as an SOCP

min_x : c^Tx ~:~ |C_i x + d_i |_2 le b_i-a_i^Tx, , ;; i=1,ldots,m,

with C_i = 0, d_i = 0, i=1,ldots,m.