A bstract We consider the static, spherically symmetric and asymptotically flat BPS extremal black holes in ungauged N = 2 D 4 supergravity theories, which scalar manifold of vector multiplets is homogeneous. By a result Shmakova on attractor equations, entropy this kind can be expressed only terms their electric magnetic charges, provided that inverse certain quadratic map (uniquely determined...

This short note extends the sparse SOS (sum of squares) and SDP (semidefinite programming) relaxation proposed by Waki, Kim, Kojima and Muramatsu for normal POPs (polynomial optimization problems) to POPs over symmetric cones, and establishes its theoretical convergence based on the recent convergence result by Lasserre on the sparse SOS and SDP relaxation for normal POPs. A numerical example i...

We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to the symmetric cone constraint. The algorithm is based on a distance-like function that is an extension of the Kullback-Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithm for convex programming with nonnegative orthant cone constraint, we sh...

We investigate the set of quantum states that can be shown to $k$-incoherent based only on their eigenvalues (equivalently, we explore which Hermitian matrices have small factor width eigenvalues). In analogy with absolute separability problem in resource theory, call these "absolutely $k$-incoherent", and derive several necessary sufficient conditions for membership this set. obtain many our r...

Lemke's algorithm for the linear complementarity problem follows a ray which leads from a certain fixed point (traditionally, the point (1,. . . , I ) ~ ) to the point given in the problem. The problem also induces a set of 2" cones, and a question which is relevant to the probabilistic analysis of Lemke's algorithm is to estimate the expected number of times a (semi-random) ray intersects the ...

*Correspondence: [email protected] 1Department of Mathematics, Indian Institute of Technology, Roorkee, 247 667, India Full list of author information is available at the end of the article Abstract In this paper, a pair of Wolfe type higher-order nondifferentiable symmetric dual programs over arbitrary cones has been studied and then well-suited duality relations have been established consider...

We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback-Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we sho...