There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear con...

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of rotating in the Einstein-scalar-Chern-Simons (EsCS) theory. In slow rotation approximation, CS term takes a linear form parameter $a$ which determines tachyonic instability. The instability for represents onset spontaneous scalarization. shown unstable against spherically symmetric sca...

In this paper we present a new algorithm for finding the unconstrained minimum of a twice–continuously differentiable function f(x) in n variables. This algorithm is based on a conic model function, which does not involve the conjugacy matrix or the Hessian of the model function. The basic idea in this paper is to accelerate the convergence of the conic method choosing more appropriate points x...

In this paper, we present a nonmonotone trust-region method of conic model for unconstrained optimization. The new method combines a new trust-region subproblem of conic model proposed in [Y. Ji, S.J. Qu, Y.J. Wang, H.M. Li, A conic trust-region method for optimization with nonlinear equality and inequality 4 constrains via active-set strategy, Appl. Math. Comput. 183 (2006) 217–231] with a non...

The purpose of this paper is to extend, as much as possible, the modern theory of condition numbers for conic convex optimization: z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ CX , to the more general non-conic format: (GPd) z∗ := minx ctx s.t. Ax− b ∈ CY x ∈ P , where P is any closed convex set, not necessarily a cone, which we call the groundset. Although any convex problem can be transformed to conic ...

In this paper we discuss the Kruppa’s equation, which is widely known as the first camera self-calibration method. The classical and the simplified version of the method are of our interest. We have analyzed it based on how it is derived. As Kruppa’s equation works based on the image of the absolute conic, which is an imaginary conic, we have found that the use of circular points at infinity wa...

We present a geometric de nition of conic sections in the oriented projective plane and describe some of their nice properties. This de nition leads to a very simple and unambiguous representation for a ne conics and conic arcs. A conic (of any type) is represented by the homogeneous coordinates of its foci and one point on it, hence, the metric plays a major role in this case as opposed to the...

A stable nanoscale thermal hot spot, with temperature approaching 100 °C, is shown to be sustained by localized Ohmic heating of a focused electric field at the tip of a slender conic nanopore. The self-similar (length-independent) conic geometry allows us to match the singular heat source at the tip to the singular radial heat loss from the slender cone to obtain a self-similar steady temperat...