Results 251 to 260 of about 850,072 (303)

Global Optimization of Polynomials over Real Algebraic Sets

Journal of Systems Science and Complexity, 2019
This paper deals with the problem of optimizing a polynomial function \(f\) over an arbitrary given real algebraic set: \(f^{*}=\inf_{x\in V} f(x)\) where \(V = \{x \in \mathbb{R}^n | g_1(x) = 0, \dots , g_s(x) = 0\}\). The authors present an algorithm to compute the global infimum \(f^*\) of \(f\) over an arbitrary given real algebraic set \(V\) where
Chu Wang, Zhi-Hong Yang, L. Zhi
semanticscholar   +2 more sources

Points near real algebraic sets

Proceedings of the American Mathematical Society, 2014
Summary: Given a real algebraic set \( X\) and a box \( \mathcal{B}\) in \( \mathbb{R}^n\), which is a union of cubes of equal size and with disjoint interiors, we bound the number of cubes that intersect \( X\). As a consequence, we bound the volume of the set of points having distance at most \( \delta \) from \( X \cap \mathcal{B}\), and we estimate
W. Schmidt, U. Zannier
semanticscholar   +3 more sources

Voronoi Diagrams of Real Algebraic Sets

Geometriae Dedicata, 2003
This paper considers Voronoi diagrams of \(n\) semialgebraic sets in \(\mathbb{R}^d\) of dimension \(d-1\). Bounds are given on the cell complexity of \(k\)th order Voronoi diagrams.
J. H. Rieger
semanticscholar   +3 more sources

The topology of real algebraic sets with isolated singularities

The Annals of Mathematics, 1981
In this paper we give a topological classification of real algebraic sets with isolated singularities, showing that they are exactly smooth closed manifolds with smooth subpolyhedra crushed to points. The question of which topological spaces are homeomorphic to real algebraic sets (solutions of polynomial equations in Euclidean space) has been long ...
S. Akbulut, H. King
semanticscholar   +2 more sources

Approximation of smooth manifolds by real algebraic sets

Russian Mathematical Surveys, 1982
This is a survey article on \(C^ r\)-approximation (with ...
N. V. Ivanov
semanticscholar   +3 more sources

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