In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...

we present an improved version of a full nesterov-todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (bull. iranian math. soc.,40(3), 541-564, (2014)). in the earlier version, each iteration consistedof one so-called feasibility step and a few -at most three -centering steps. here, each iteration consists of only a feasibilitystep. thus, the new alg...

‎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...

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = ∏ i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for R+. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence ...

A one{to{one relation is established between the nonnegative spectral values of a vector in a primitive symmetric cone and the eigenvalues of its quadratic representation. This result is then exploited to derive similarity relations for vectors with respect to a general symmetric cone. For two positive deenite matrices X and Y , the square of the spectral geometric mean is similar to the matrix...

Abstract Let ? be a proper open cone in real Banach space V . We show that the tube domain V ? i ? ? {V\oplus i\Omega} over is biholomorphic to bounded symmetric if and only normal linearly homogeneous Finsler cone, which equiva...