We propose solving the inverse eigenvalue problem for symmetric nonnegative matrices by means of a di erential equation. If the given spectrum is feasible, then a symmetric nonnegative matrix can be constructed simply by following the solution curve of the di erential system. The choice of the vector eld is based on the idea of minimizing the distance between the cone of symmetric nonnegative m...

Extending the previous work of Monteiro and Pang (1998), this paper studies properties of fundamental maps that can be used to describe the central path of the monotone nonlinear complementarity problems over the cone of symmetric positive semidefinite matrices. Instead of focusing our attention on a specific map as was done in the approach of Monteiro and Pang (W98), this paper considers a gen...

This paper focuses on the study of the second-order directional derivative of a symmetric matrix-valued function of the form F (X) = Pdiag[f(λ1(X)), · · · , f(λn(X))]P . For this purpose, we first adopt a direct way to derive the formula for the second-order directional derivative of any eigenvalue of a matrix in Torki [13]; Second, we establish a formula for the (parabolic) second-order direct...

The notion of “strong stability” has been introduced in a recent paper [KHP2]. This notion is relevant for state-space models described by physical variables and prohibits overshooting trajectories in the state-space transient response for arbitrary initial conditions. Thus, “strong stability” is a stronger notion compared to alternative definitions (e.g. stability in the sense of Lyapunov or a...

The Generalized Lax Conjecture asks whether every hyperbolicity cone is a section of a semidefinite cone of sufficiently high dimension. We prove that the space of hyperbolicity cones of hyperbolic polynomials of degree d in n variables contains (n/d) pairwise distant cones in the Hausdorff metric, and therefore that any semidefinite representation of such polynomials must have dimension at lea...

In the solution methods of the symmetric cone complementarity problem (SCCP), the squared norm of a complementarity function serves naturally as a merit function for the problem itself or the equivalent system of equations reformulation. In this paper, we study the growth behavior of two classes of such merit functions, which are induced by the smooth EP complementarity functions and the smooth...

The theory of the dielectric cone antenna has been known since the early seventies. On their own, this antenna has a reasonably circular symmetric radiation pattern but exhibits an undesirably high side-lobe level. A properly designed metallic shield, which does not interfere with the field structure of the dielectric cone, may be used to reduce the side-lobe level. Although in principle this a...

Introduction Efficient fitting of quadric surfaces to unstructured point clouds or triangle meshes is an important component of many reverse engineering systems [6]. Users may prefer a given surface be fit by a specific quadric type: for example, they may want to ensure the quadric is a cone, ellipsoid, or a rotationally-symmetric subtype (spheroid, circular cone, etc). Methods for type-specifi...

This article studies a pair of higher order nondifferentiable symmetric fractional programming problem over cones. First, cone convex function is introduced. Then using the properties this function, duality results are set up, which give legitimacy primal dual model.

We give an overview of cone optimization software, with special attention to the differences between the existing packages. We assume the reader is familiar with the theory and algorithms of cone optimization, thus technical details are kept at a minimum. We also outline current research trends and area of potential improvement. 1 Problem description Conic optimization solvers target problems o...