Second-Order Cone Problems (SOCP)

• A linear function is minimized over the intersection of an affine set and the product of second-order (quadratic) cones
• Nonlinear, convex problem including linear and (convex) quadratic programs as special cases
• Solved by efficient primal-dual interior-point methods
• Number of iterations required to solve a problem grows at most as the square root of the problem size
• Typical number of iterations ranges between 5 and 50, almost independent of the problem size

See ``Applications of second-order cone programming'' [144,21] and also Prof. Stephen Boyd's course on convex optimization:
http://www.stanford.edu/class/ee364/.

• LIPSOL: Matlab code for linear programming using interior point methods.
• Matlab's linprog (in the Optimization Tool Box)
• Octave's lp (SourceForge package)

See §3.13 for examples of optimal FFT window design using linprog.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.