Let C be a full dimensional, closed, pointed and convex cone in a nite dimensional real vector space E with an inner product hx;yi of x; y 2 E , andM a maximal monotone subset of E E . This paper studies the existence and continuity of centers of the monotone generalized complementarity problem associated with C and M: Find (x;y) 2 M\ (C C ) such that hx;yi = 0. Here C = fy 2 E : hx;yi 0 for al...

In these notes we investigate the cone of nef curves of projective varieties, which is the dual cone to the cone of pseudo-effective divisors. We prove a structure theorem for the cone of nef curves of projective Q-factorial klt pairs of arbitrary dimension from the point of view of the Minimal Model Program. This is a generalization of Batyrev’s structure theorem for the cone of nef curves of ...

Concerning with the topics of fuzzy decision processes, a brief survey on ordering of fuzzy numbers on R is presented and an extension to that of fuzzy sets(numbers) on Rn are considered. This extension is a pseudo order 4 K de ned by a non-empty closed convex cone K and characterized by the projection into its dual cone K. Especially a structure of the lattice is presented on the class of rect...

Copositive optimization is a quickly expanding scientific research domain with wide-spread applications ranging from global nonconvex problems in engineering to NP-hard combinatorial optimization. It falls into the category of conic programming (optimizing a linear functional over a convex cone subject to linear constraints), namely the cone C of all completely positive symmetric n×n matrices (...

We consider the problem of finding the nearest point in a polyhedral cone C = {x ∈ Rn : Dx ≤ 0} to a given point b ∈ Rn, where D ∈ Rm×n. This problem can be formulated as a convex quadratic programming problem with special structure. We study the structure of this problem and its relationship with the nearest point problem in a pos cone through the concept of polar cones. We then use this relat...

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X−E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F -harmonic functions (solutions) wh...

Let F be a fully nonlinear second-order partial differential subequation of degenerate elliptic type on a manifold X. We study the question: Which closed subsets E ⊂ X have the property that every F -subharmonic function (subsolution) on X − E, which is locally bounded across E, extends to an F -subharmonic function on X. We also study the related question for F harmonic functions (solutions) w...

With the objective of minimizing the total execution time of a parallel program on a distributed memory parallel computer, this paper discusses the selection of an optimal supernode shape of a supernode transformation (also known as tiling). We assume that the communication cost is dominated by the startup penalty and therefore, can be approximated by a constant. We identify three parameters of...

Abstract We investigate the weighted $L_p$ affine surface areas which appear in recently established Steiner formula of Brunn–Minkowski theory. show that they are valuations on set convex bodies and prove isoperimetric inequalities for them. related to f divergences cone measures body its polar, namely Kullback–Leibler divergence Rényi divergence.