TY - JOUR
T1 - Construction of proximal distances over symmetric cones
AU - López, Julio
AU - Quiroz, Erik Alex Papa
PY - 2017/8/3
Y1 - 2017/8/3
N2 - © 2017 Informa UK Limited, trading as Taylor & Francis Group. This paper is devoted to the study of proximal distances defined over symmetric cones, which include the non-negative orthant, the second-order cone and the cone of positive semi-definite symmetric matrices. Specifically, our first aim is to provide two ways to build them. For this, we consider two classes of real-valued functions satisfying some assumptions. Then, we show that its corresponding spectrally defined function defines a proximal distance. In addition, we present several examples and some properties of this distance. Taking into account these properties, we analyse the convergence of proximal-type algorithms for solving convex symmetric cone programming (SCP) problems, and we study the asymptotic behaviour of primal central paths associated with a proximal distance. Finally, for linear SCP problems, we provide a relationship between the proximal sequence and the primal central path.
AB - © 2017 Informa UK Limited, trading as Taylor & Francis Group. This paper is devoted to the study of proximal distances defined over symmetric cones, which include the non-negative orthant, the second-order cone and the cone of positive semi-definite symmetric matrices. Specifically, our first aim is to provide two ways to build them. For this, we consider two classes of real-valued functions satisfying some assumptions. Then, we show that its corresponding spectrally defined function defines a proximal distance. In addition, we present several examples and some properties of this distance. Taking into account these properties, we analyse the convergence of proximal-type algorithms for solving convex symmetric cone programming (SCP) problems, and we study the asymptotic behaviour of primal central paths associated with a proximal distance. Finally, for linear SCP problems, we provide a relationship between the proximal sequence and the primal central path.
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85009257879&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85009257879&origin=inward
U2 - 10.1080/02331934.2016.1277998
DO - 10.1080/02331934.2016.1277998
M3 - Article
SN - 0233-1934
SP - 1301
EP - 1321
JO - Optimization
JF - Optimization
ER -