Work

Refining the partition for multifold conic optimization problems

Year: 2018

Type: preprint

Abstract: In this paper we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in [J. F. Bonnans and H. Ramírez C., Math. Program. 104 (2005), no. 2-3, Ser. B, 205--227] for conic optimization problems, and in [J. Peña and V. Roshchina, Math. Program. 142 (2013), no 1-2, Ser. A, 579--589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework, and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1804.00386

Authors: Ramírez, Héctor, Roshchina, Vera