Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.

We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and an algorithm for computing the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces (= the set of points w...

During the last two decades, major developments in convex optimization were focusing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex program and to exploit this structure in order to process the program efficiently. In the paper, we overview the major components of...

One task of all Fortran 90 compilers is to scalarize the array syntax statements of a program into equivalent sequential code. Most compilers require multiple passes over the program source to ensure correctness of this translation, since their analysis algorithms only work on the scalarized form. These same compilers then make additional subsequent passes to perform loop optimizations such as ...

We present an efficient geometric algorithm for conic spline curve fitting and fairing through conic arc scaling. Given a set of planar points, we first construct a tangent continuous conic spline by interpolating the points with a quadratic Bézier spline curve or fitting the data with a smooth arc spline. The arc spline can be represented as a piecewise quadratic rational Bézier spline curve. ...

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...