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

Second-Order Cone Programming

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The second-order cone in mathbf{R}^3 is the set of vectors (x_1,x_2,y) with y ge sqrt{x_1^2+x_2^2}. The picture shows part of the cone, and a slice (at y=1). For some strange reason, this set is called an ‘‘ice-cream cone’’.

Second-order cone programming (SOCP) is a generalization of linear and quadratic programming that allows for affine combination of variables to be constrained inside second-order cones. The SOCP model includes as special cases problems with convex quadratic objective and constraints.

SOCP models are particularly useful in geometry problems, as well as in linear programs where the data is imprecisely known. We explore this further here.

Outline