Displaying similar documents to “Full-Newton step infeasible interior-point algorithm for SDO problems”

Goffin's algorithm for zonotopes

Michal Černý (2012)

Kybernetika

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The Löwner-John ellipse of a full-dimensional bounded convex set is a circumscribed ellipse with the property that if we shrink it by the factor n (where n is dimension), we obtain an inscribed ellipse. Goffin’s algorithm constructs, in polynomial time, a tight approximation of the Löwner-John ellipse of a polyhedron given by facet description. In this text we adapt the algorithm for zonotopes given by generator descriptions. We show that the adapted version works in time polynomial...

On the number of abelian groups of a given order (supplement)

Hong-Quan Liu (1993)

Acta Arithmetica

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1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, A ( x ) = C ₁ x + C ₂ x 1 / 2 + C ₃ x 1 / 3 + O ( x 50 / 199 + ε ) , where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented...

Reference points based recursive approximation

Martina Révayová, Csaba Török (2013)

Kybernetika

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The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant...