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 consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...

where w = √ 1 + |Du|2, ν = (Du/w,−1/w) denotes the downwards directed unit normal on the spatial graph Su of the function u, κ = κ[u] = (κ1, . . . , κn) denotes the n-tuple of principal curvatures of Su with respect to the upward normal, and f is a smooth symmetric function with some special properties as in [1], which is defined in an open convex symmetric cone Γ ⊂ R with vertex at the origin....

We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones (e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetri...

The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Conservation laws and a priori estimates of smooth solutions are first derived in a formal way. In the spherically symmetr...

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett’s decomposition and an unbiased risk estimate formula for a general family of Wishart distributions on the irreducible symmetric...

A well-known result of Lyapunov on continuous linear systems asserts that a real square matrix A is positive stable if and only if for some symmetric positive definite matrix X, AX + XA is also positive definite. A recent result of Moldovan-Gowda says that a Z-matrix A is positive stable if and only if for some symmetric strictly copositive matrix X, AX + XA is also strictly copositive. In this...

Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry, and modeling the compression by suitable Dirichlet boundary conditions at the center and the boundary of the sheet, we identify the energy scaling law in the...

We give explicit polynomial-sized (in n and k) semidefinite representations of the hyperbolicity cones associated with the elementary symmetric polynomials of degree k in n variables. These convex cones form a family of non-polyhedral outer approximations of the non-negative orthant that preserve low-dimensional faces while successively discarding high-dimensional faces. More generally we const...

It is clear Ce(f) is invariant under scaling by R>0 and open. Further, this cone is convex. Its closure is basic semialgebraic with all faces exposed, but we shall not elaborate on these points. The first examples of hyperbolic polynomials are familiar from optimization. Example 12.2. Let f = ∏n i=1 xi ∈ R[x1, . . . , xn]n and e = (1, . . . , 1). Then f is hyperbolic with respect to e and the h...

We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof stems in a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.