Related papers: Circumcentric directions of cones
We define the finest order on inductive limits of ordered cones which makes the linear mappings monotone and gives rise to the definition of inductive limit topologies for cones. Using the polars of neighborhoods, we establish embeddings…
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…
Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones.
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spanned vector space) into which it embeds as a generating…
Circumcenters play an important role in the design and analysis of accelerating various iterative methods in optimization. In this work, we propose Bregman (pseudo-)circumcenters associated with finite sets. We show the existence and give…
In this note we characterize isoperimetric regions inside almost-convex cones. More precisely, as in the case of convex cones, we show that isoperimetric sets are given by intersecting the cone with a ball centered at the origin.
We consider the optimal containment of polygonal regions within convex containers with the special property of 'orientedness' - an oriented region enables us to choose a preferred direction on the plane (this direction is not necessarily an…
We develop a natural generalization to the notion of the central path -- a notion that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the "derivative cones" of a "hyperbolicity…
We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
Tensor products of convex cones have recently come up in different areas, ranging from functional analysis and operator theory to approximation theory and theoretical physics. However, most of the existing literature focuses either on…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic…
We provide a unified framework for a systematic analysis of the existence of solutions to general nonconvex problems, relying on asymptotic and retractive cones for functions and sets. Using this framework we develop new necessary and…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…
The Circumcentered Reflection Method (CRM) is a recently developed projection method for solving convex feasibility problems. It offers preferable convergence properties compared to classic methods such as the Douglas-Rachford and the…
A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…