Artículo de revista
Refining the partition for multifold conic optimization problems
Date
2020Registration in:
Optimization Volumen: 69 Número: 11 Páginas: 2489-2507 Oct 2020
10.1080/02331934.2020.1822835
Author
Ramírez Cabrera, Héctor
Roshchina, Vera
Institutions
Abstract
In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramirez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2-30):205-227] for conic optimization problems, and in Pena and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1-2):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.