A SOCP (or Second Order Cone Program ) is a problem in mathematical optimization in which the solution to the problem is not only subject to linear restrictions, but should also lie in a certain cone . This cone is called the second-order cone in English, from which the name of the program is derived.
is. Here is the n-dimensional identity matrix . In this case, every cone restriction can be replaced by a quadratic and a linear restriction.
If all are equal to zero, the inequality restrictions can be reformulated as . If one now combines the left side of the inequality for all into a vector and the right line into a matrix that consists of the vectors line by line , then the SOCP can be formulated as a linear optimization problem.
literature
Boyd, Stephen; Vandenberghe, Lieven (2004). Convex Optimization. Cambridge University Press. ISBN 978-0-521-83378-3 . ( online )