This paper examines an observable consequence for the diffuse extragalactic background radiation (EGBR) of the hypothesis that if closed, our universe possesses time symmetric boundary conditions. By reason of theoretical and observational clarity, attention is focused on optical wavelengths. The universe is modeled as closed Friedmann-Robertson-Walker. It is shown that, over a wide range of fr...

In this paper we construct two approximation hierarchies for the completely positive cone based on symmetric tensors. We show that one hierarchy corresponds to dual cones of a known polyhedral approximation hierarchy for the copositive cone, and the other hierarchy corresponds to dual cones of a known semidefinite approximation hierarchy for the copositive cone. As an application, we consider a...

A symmetric matrix is defined to be completely positive if it allows a factorisation BB , where B is an entrywise nonnegative matrix. This set is useful in certain optimisation problems. The interior of the completely positive cone has previously been characterised by Dür and Still [M. Dür and G. Still, Interior points of the completely positive cone, Electronic Journal of Linear Algebra, 17:48...

A symmetric matrix A is completely positive (CP) if there exists an entrywise nonnegative matrix B such that A = BB . We characterize the interior of the CP cone. We formulate the problem as linear optimizations with cones of moments. A semidefinite algorithm is proposed for checking interiors of the CP cone, and its properties are studied. A CP-decomposition of a matrix in Dickinson’s form can...

A symmetric matrix is defined to be completely positive if it allows a factorisation BB , where B is an entrywise nonnegative matrix. This set is useful in certain optimisation problems. The interior of the completely positive cone has previously been characterised by Dür and Still [M. Dür and G. Still, Interior points of the completely positive cone, Electronic Journal of Linear Algebra, 17:48...

Notation: The set of real symmetric n ×n matrices is denoted S . A matrix A ∈ S is called positive semidefinite if x Ax ≥ 0 for all x ∈ R, and is called positive definite if x Ax > 0 for all nonzero x ∈ R . The set of positive semidefinite matrices is denoted S and the set of positive definite matrices + n is denoted by S++. The cone S is a proper cone (i.e., closed, convex, pointed, and solid). +

Abstract In this article, we present generalizations of the cone-preinvexity functions and study a pair second-order symmetric solutions for multiple objective nonlinear programming problems under these functions. addition, establish prove theorems weak duality, strong strict converse self-duality by assuming skew-symmetric Finally, provide four nontrivial numerical examples to demonstrate that...

This paper extends the regularized smoothing Newton method in vector optimization to symmetric cone optimization, which provide a unified framework for dealing with the nonlinear complementarity problem, the second-order cone complementarity problem, and the semidefinite complementarity problem (SCCP). In particular, we study strong semismoothness and Jacobian nonsingularity of the total natura...

The purpose of this paper is to introduce second order (K, F)-pseudoconvex and second order strongly (K, F)pseudoconvex functions which are a generalization of cone-pseudoconvex and strongly cone-pseudoconvex functions. A pair of second order symmetric dual multiobjective nonlinear programs is formulated by using the considered functions. Furthermore, the weak, strong and converse duality theor...

In this paper, we consider the mathematical program with symmetric cone complementarity constraints (MPSCCC) in a general form. It includes the mathematical program with second-order-cone complementarity constraints (MPSOCCC) and the mathematical program with complementarity constraints (MPCC). We present a smoothing method which approximates the primal MPSCCC by means of the ChenMangasarian cl...