This article deals with linear complementarity problems over symmetric cones. Our objective here is to characterize global uniqueness and solvability properties for linear transformations that leave the symmetric cone invariant. Specifically, we show that, for algebra automorphisms on the Lorentz space Ln and for quadratic representations on any Euclidean Jordan algebra, global uniqueness, glob...

A Mond–Weir type multiobjective variational mixed integer symmetric dual program over arbitrary cones is formulated. Applying the separability and generalized F-convexity on the functions involved, weak, strong and converse duality theorems are established. Self duality theorem is proved. A close relationship between these variational problems and static symmetric dual minimax mixed integer mul...

The von Neumann entropy of pure quantum states and the min-cut function weighted hypergraphs are both symmetric submodular functions. In this article, we explain coincidence by proving that any hypergraph can be approximated (up to an overall rescaling) entropies known as stabilizer states. We do so constructing a novel ensemble random states, built from tensor networks, whose entanglement stru...

In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Function is nondecreasing by explicitly computing it. also compute standard bases these toric ideals.

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...

We develop a natural variant of Dikin’s affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous polynomial-time affine-scaling algorithms have been for conic optimization problems in which the underlying cone is symmetric. Hyperbolicity cones, however, need not be...

In this work, we continue the investigation of algebraic properties Gårding cones in space symmetric matrices. Based on theory, propose a new approach to study fully nonlinear differential operators and second-order partial equations. We prove comparison theorems type for evolution Hessian establish relation between Bellman

Abstract. We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]. Under suitable second order pseudo-invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. Our symmetric duality...

We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric matrices with factor width at most two is exactly the class of (possibly singular) symmetric H-matrices (also known as generalized diagonally dominant matrices) with positive diagonals, H+. We prove b...

We prove central limit theorems of Lindeberg-L evy and Lindeberg-Feller type for any K-invariant random variables on all irreducible symmetric spaces and irreducible symmetric cones, completing in this way the numerous partial results known before. In all cases the limit measures turn out to be Gaussian and being such a limit characterizes these measures. On the other hand we show that other cl...