In this paper we study plane conic geometry, particularly different representations of geometric constructions and relations in plane conic geometry, with Cayley and bracket algebras. We propose three powerful simplification techniques for bracket computation involving conic points, and an algorithm for rational Cayley factorization in conic geometry. The factorization algorithm is not a genera...

It is not straightforward to find a new feasible solution when several conic constraints are added to a conic optimization problem. Examples of conic constraints include semidefinite constraints and second order cone constraints. In this paper, a method to slightly modify the constraints is proposed. Because of this modification, a simple procedure to generate strictly feasible points in both t...

An approach for reconstructing wireframe models of curvilinear objects from three orthographic views is discussed. Our main stress is on the method of generating three-dimensional (3D) conic edges from twodimensional (2D) projection conic curves, which is the pivotal work for reconstructing curvilinear objects from three orthographic views. In order to generate 3D conic edges, a five-point meth...

1077-3142/$ see front matter 2011 Elsevier Inc. A doi:10.1016/j.cviu.2011.07.004 ⇑ Corresponding author. E-mail addresses: [email protected] [email protected] (A. Yilmaz). This paper introduces a new representation for planar objects which is invariant to projective transformation. Proposed representation relies on a new shape basis which we refer to as the conic basis. The conic basis ta...

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable wit...

In this paper we consider an aggregation technique introduced by Yıldıran [45] to study the convex hull of regions defined by two quadratic inequalities or by a conic quadratic and a quadratic inequality. Yıldıran [45] shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We show how this aggregation technique...

Spontaneous scalarization is a gravitational phenomenon in which deviations from general relativity arise once certain threshold curvature exceeded, while being entirely absent below that threshold. For black holes, known to be triggered by coupling between scalar and the Gauss-Bonnet invariant. A with Ricci scalar, can trigger neutron stars, instead not contribute onset of hole scalarization, ...

The objective of this paper is to deal with the fuzzy conic programming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a specific ordering cone is established based on the parameterized representation of fuzzy numbers. Under this setting, duality theo...

In this paper, we study cut generating functions for conic sets. Our first main result shows that if the conic set is bounded, then cut generating functions for integer linear programs can easily be adapted to give the integer hull of the conic integer program. Then we introduce a new class of cut generating functions which are non-decreasing with respect to second-order cone. We show that, und...