Second-Order Cone Problems
In 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 [153,22]. Nonlinear, convex problem including linear and (convex) quadratic programs are special cases. SOCP problems are solved by efficient primal-dual interior-point methods. The number of iterations required to solve a problem grows at most as the square root of the problem size. A typical number of iterations ranges between 5 and 50, almost independent of the problem size.
Resources
- LIPSOL: Matlab code for linear programming using interior point methods.
- Matlab's linprog (in the Optimization Toolbox)
- Octave's lp (SourceForge package)
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