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...

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...

An occluding contour of a sphere is projected to a conic in the perspective image, and such a conic is called a sphere image. Recently, it has been discovered that each sphere image is tangent to the image of the absolute conic at two double-contact image points. The double-contact theorem describes the properties of three conics which all have double contact with another conic. This theorem pr...

Traditionally, Multi-task Learning (MTL) models optimize the average of task-related objective functions, which is an intuitive approach and which we will be referring to as Average MTL. However, a more general framework, referred to as Conic MTL, can be formulated by considering conic combinations of the objective functions instead; in this framework, Average MTL arises as a special case, when...

We consider the problem of fitting a conic to a set of 2D points. It is commonly agreed that minimizing geometrical error, i.e. the sum of squared distances between the points and the conic, is better than using an algebraic error measure. However, most existing methods rely on algebraic error measures. This is usually motivated by the fact that pointto-conic distances are difficult to compute ...

We study approximation and localized polynomial frames on a bounded double hyperbolic or conic surface the domain by such hyperplanes. The main work follows framework developed recently in Xu (J Funct Anal 281(12):109257, 2021) for homogeneous spaces that are assumed to contain highly kernels constructed via family of orthogonal polynomials. existence will be established with help closed-form f...