The purpose of this survey article is to introduce the reader to a very elegant formulation of convex optimization problems called conic optimization and outline its many advantages. After a brief introduction to convex optimization, the notion of convex cone is introduced, which leads to the conic formulation of convex optimization problems. This formulation features a very symmetric dual prob...

A framework is developed for the design and analysis of single-viewpoint catadioptric cameras that use two or more mirrors. The use of multiple mirrors permits folding of the optics which leads to more compact camera designs than ones that use a single mirror. A dictionary of camera designs that use two conic mirrors is presented. We show that any folded system that uses conic mirrors has a geo...

A public key cryptosystem scheme is proposed that are based on conic curves over the ring Zn. Our scheme is motivated by KMOV scheme on elliptic curves, but our scheme remove some restrictive condition from KMOV scheme and constructed on conic curves. Its security bases on the difficulty of factoring a composite number n, just like RSA. It can resist some of the known attacks on RSA. We also co...

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε +O(1), if the spline consists of parabolic arcs, and c2ε + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We also show that...

In this paper it is shown how to use corresponding conics in two images to estimate the epipolar geometry, the fundamental/essential matrix and reconstruct the scene. The corresponding conics can be images of either a planar conic or silhouettes of a quadric. It is shown that one conic correspondence gives two constraints on the fundamental matrix and a method to estimate the fundamental matrix...

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to linear programming problem with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc). The ...

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions f...

In the so-called conformal model of Euclidean space of geometric algebra, circles receive a very elegant description by the outer product of three general points of that circle, forming what is called a tri-vector. Because circles are a special kind of conic section, the question arises, whether in general some kind of third order outer product of five points on a conic section (or certain line...

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε − 1 4 + O(1), if the spline consists of parabolic arcs, and c2ε − 1 5 + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We a...

Two computing approaches, based on linear and conic splines, are proposed here in reviewed and extended for vectorizing image outlines. Both of the approaches have various phases including extracting outlines of images, detecting corner points from the detected outlines, and curve fitting. Interpolation splines are the bases of the two approached. Linear spline approach is straight forward as i...