Fitting of conics to a set of points is a well researched area and is used in many fields of science and engineering. Least squares methods are one of the most popular techniques available for conic fitting and among these, orthogonal distance fitting has been acknowledged as the ’best’ least squares method. Although the accuracy of orthogonal distance fitting is unarguably superior, the proble...

In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the cone used is not...

In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified framework for conic and Lagrangian-conic relaxations of quadratic optimization problems (QOPs) and polynomial optimization problems (POPs). The framework is constructed with a linear conic optimization problem (COP) in a finite dimensional vector space endowed with an inner product, where the cone used is not...

Parallax displacement is used to determine a relative 3D conic projective structure. This value is invariant between any number of views in time if the conic is not moving with respect to the plane of the homography. It can be used to determine conic correspondence between three simultaneous views. The corresponding conics may then be used to determine the epipolar geometry. This method of dete...

The occurrence frequencies of dayside ion conics with various conic angles are obtained as a function of altitude from Exos-D (Akebono) observations. We made a model calculation of ion conic evolution to match the observation results. The observed occurrence frequencies of ion conics with 80 to 90 conic angle are used as an input to the model and the occurrence frequencies of ion conics with sm...

We present a framework for designing and analyzing primal-dual interior-point methods for convex optimization. We assume that a self-concordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techniques of interior-point methods to the given good formulation of the problem (as is, without a conic...

We study the order of maximizers in linear conic programming (CP) as well as stability issues related to this. We do this by taking a semi-infinite view on conic programs: a linear conic problem can be formulated as a special instance of a linear semi-infinite program (SIP), for which characterizations of the stability of first order maximizers are well-known. However, conic problems are highly...