Keywords: Conic sections Bézier curves Eccentricity Asymptotes Axes Foci In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in Bézier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the use of coordinates.

We investigate the derivation of disjunctive conic cuts for mixed integer second order cone optimization (MISOCO). These conic cuts characterize the convex hull of the intersection of a disjunctive set and the feasible set of a MISOCO problem. We present a full characterization of these inequalities when the disjunctive set considered is defined by parallel hyperplanes.

It is known that linear conic systems are a special case of setvalued sublinear mappings. Hence the latter subsumes the former. In this note we observe that linear conic systems also contain set-valued sublinear mappings as a special case. Consequently, the former also subsumes the latter.

A surface generated by a one parameter family of conics c(t) is called conic surface. If c(t) can be described by rational functions, the generated conic surface is rational. An algorithm to construct real rational parametrizations for such surfaces and some examples will be given.

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD(Computer Aided Geometric Design). We also present the numerical results for these appli...

Linear programming duality yields e,cient algorithms for solving inverse linear programs. We show that special classes of conic programs admit a similar duality and, as a consequence, establish that the corresponding inverse programs are e,ciently solvable. We discuss applications of inverse conic programming in portfolio optimization and utility function identi0cation. c © 2004 Elsevier B.V. A...

In this work, generalization ability of a hybrid neural network algorithm is investigated. This algorithm consists of a combination of Radial Basis Function (RBF) and Multilayer Perceptron (MLP) in one single network using conic section functions. The network architecture using this algorithm is called Conic Section Function Neural Network (CSFNN). Various problems are examined to demonstrate t...