The second-order cone programming problem is reformulated into several new systems of nonlinear equations. Assume the perturbation of the data is in a certain neighborhood of zero. Then starting from a solution to the old problem, the semismooth Newton’s iterates converge Q-quadratically to a solution of the perturbed problem. The algorithm is globalized. Numerical examples show that the algorithm is good for “warm starting” — for some instances, the solution of a perturbed problem is hit in two iterations.
Citation
AdvOl-Report#2004/17 McMaster University, Advanced Optimization Laboratory Hamilton, Ontario, Canada October 2004