An Algorithm for Perturbed Second-order Cone Programs

Yu Xia (yuxiacas.mcmaster.ca)

Abstract: 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.

Keywords: Second-order cone, complementarity, semismooth, warm start, Newton's method

Category 1: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Complementarity and Variational Inequalities

Citation: AdvOl-Report#2004/17 McMaster University, Advanced Optimization Laboratory Hamilton, Ontario, Canada October 2004

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Entry Submitted: 10/16/2004
Entry Accepted: 10/16/2004
Entry Last Modified: 10/16/2004

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