Results 101 to 110 of about 868 (134)

Tangent Cones and Tangent Sets

2014
Tangent cones of first-order and tangent cones and tangent sets of higher-order play a very important role in set-valued optimization. For instance, derivatives and epiderivatives of set-valued maps are commonly defined by taking tangent cones and tangent sets of graphs and epigraphs of set-valued maps. Moreover, properties of tangent cones and tangent
Akhtar A. Khan, Christiane Tammer, Constantin Zălinescu   +2 more
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The Quantificational Tangent Cones

Canadian Journal of Mathematics, 1988
Nonsmooth analysis has provided important new mathematical tools for the study of problems in optimization and other areas of analysis [1, 2, 6-12, 28]. The basic building blocks of this subject are local approximations to sets called tangent cones.Definition 1.1. Let E be a real, locally convex, Hausdorff topological vector space (abbreviated l.c.s.).
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Non‐archimedean stratifications of tangent cones

Mathematical Logic Quarterly, 2017
AbstractWe study the impact of a kind of non‐archimedean stratifications (t‐stratifications) on tangent cones of definable sets in real closed fields. We prove that such stratifications induce stratifications of the same nature on the tangent cone of a definable set at a fixed point.
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Comparing New Notions of Tangent Cones

Journal of the London Mathematical Society, 1989
New notions of tangent cones which have been recently introduced are related. These notions are variants of the Clarke's strict tangent cone and give rise to corresponding generalized derivatives. They are closed, convex and larger than the Clarke strict tangent cone, what are desirable features.
Jofré, Alejandro, Penot, Jean-Paul
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THE STRUCTURE OF THE TANGENT CONE: AN INTERESTING BIJECTION#

Communications in Algebra, 2005
ABSTRACT Let X = Spec(R) be a reduced equidimensional algebraic variety over an algebraically closed field k. Let Y = Spec(R/𝔮) be a codimension one ordinary multiple subvariety, where 𝔮 is a prime ideal of height 1 of R. If U is a nonempty open subset of Y and 𝔪 a closed point of U, we denote by A ≅ R 𝔪 its local ring ...
ILARDI, GIOVANNA, CASTALDO G.
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The virtues of laziness: Complexity of the Tangent Cone Algorithm

Applicable Algebra in Engineering, Communication and Computing, 1993
The study of computational problems in the ideal theory of local rings led to the notion of standard bases. These are a version of Gröbner bases for orderings which are not well orderings. In most cases appearing in applications, the tangent cone algorithm computes a standard basis of a given ideal [\textit{T. Mora}, \textit{G.
Abdallah Assi, Teo Mora
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On a characterization of Clarke's tangent cone

Journal of Optimization Theory and Applications, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
GIORGI G., GUERRAGGIO, ANGELO
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On semialgebraic tangent cones

1998
Summary: The paper deals with the following question: Which semialgebraic subsets of \(\mathbb{R}^n\) can be realized as tangent cones to real algebraic subsets of \(\mathbb{R}^n\)? At first we prove that the answer is positive for every closed semialgebraic cone in \(\mathbb{R}^n\) of dimension \(\leq 2\). Then, for closed semialgebraic cones \(A\) in
FERRAROTTI M, FORTUNA, ELISABETTA
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Intersection multiplicities and tangent cones

Mathematical Proceedings of the Cambridge Philosophical Society, 1979
The following result has at least the appeal of intuitive plausibility. Let U and V be subvarieties of an algebraic variety X; let x ∈ X be an isolated point of the intersection of U and V, and let I(X, U. V, x) denote the intersection multiplicity (in some sense to be made precise) of U and V at x.
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Singular Points and Tangent Cones

1992
The Zariski tangent space to a variety X ⊂ 𝔸n at a point p is described by taking the linear part of the expansion around p of all the functions on 𝔸n vanishing on X. In case p is a singular point of X, however, this does not give us a very refined picture of the local geometry of X; for example, if X ⊂ 𝔸2 is a plane curve, the Zariski tangent space to
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