The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the second-order cone linear complementarity problems (SOCLCP) ...

Euclidean Jordan-algebra is a commonly used tool in designing interiorpoint algorithms for symmetric cone programs. T -algebra, on the other hand, has rarely been used in symmetric cone programming. In this paper, we use both algebraic characterizations of symmetric cones to extend the target-following framework of linear programming to symmetric cone programming. Within this framework, we desi...

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is √ log , where ...

Bessel functions of matrix argument appeared as a subject of studies in the work of Herz [6]. One can find in the multivariate statistics literature some applications of these functions (see [11]). The main tool of Herz’s work was the Laplace transform and its inverse in the space of real symmetric matrices. He obtained several properties but a “good” differential system was lacking. This was t...

We determine the causal transformations of a class of causal symmetric spaces (Th. 2.4.1). As a basic tool we use causal imbeddings of these spaces as open orbits in the conformal compactification of Euclidean Jordan algebras. In the first chapter we give elementary constructions of such imbeddings for the classical matrix-algebras. In the second chapter we generalize these constructions for ar...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

In this paper we shall study the multipliers on Banach algebras and We prove some results concerning Arens regularity and amenability of the Banach algebra M(A) of all multipliers on a given Banach algebra A. We also show that, under special hypotheses, each Jordan multiplier on a Banach algebra without order is a multiplier. Finally, we present some applications of m...

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.