Open AccessBook
Nonlinear Programming
TLDR
It is shown that if A is closed for all k → x x, k → y y, where ( k A ∈ ) k y x , then ( ) A ∉ y x .Abstract:
Part 1 (if): Assume that Z is closed. We must show that if A is closed for all k → x x , k → y y , where ( k A ∈ ) k y x , then ( ) A ∈ y x . By the definition of Z being closed, we know that all points arbitrarily close to Z are in Z. Let k → x x , k → y y , and ( k A ∈ ) k y x . Now, for any ε > 0, there exists an N such that for all k ≥ N we have || || k ε − < x x , || || k ε − < y y which implies that ( ) , x y is arbitrarily close to Z, so ( ) , x y ∈ Z and ( ) A ∈ y x . Thus, A is closed.read more
Citations
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Journal ArticleDOI
A Tutorial on Support Vector Machines for Pattern Recognition
TL;DR: There are several arguments which support the observed high accuracy of SVMs, which are reviewed and numerous examples and proofs of most of the key theorems are given.
Journal ArticleDOI
A tutorial on support vector regression
TL;DR: This tutorial gives an overview of the basic ideas underlying Support Vector (SV) machines for function estimation, and includes a summary of currently used algorithms for training SV machines, covering both the quadratic programming part and advanced methods for dealing with large datasets.
Journal ArticleDOI
Convergence of a block coordinate descent method for nondifferentiable minimization
TL;DR: In this article, the convergence properties of a block coordinate descent method applied to minimize a non-convex function f(x1,.., x 2, N 3 ) with certain separability and regularity properties were studied.
Book ChapterDOI
A Generalized Representer Theorem
TL;DR: The result shows that a wide range of problems have optimal solutions that live in the finite dimensional span of the training examples mapped into feature space, thus enabling us to carry out kernel algorithms independent of the (potentially infinite) dimensionality of the feature space.
Proceedings ArticleDOI
Regularized multi--task learning
TL;DR: An approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines, that have been successfully used in the past for single-- task learning is presented.
References
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How good is the simplex algorithm
Victor Klee,George J. Minty +1 more
TL;DR: By constructing long 'increasing' paths on appropriate convex polytopes, it is shown that the simplex algorithm for linear programs is not a 'good algorithm' in the sense of J. Edmonds.