Abstract
In this book letters x,y, ... are scalars (real numbers) and the letters in bold italics, x, y, ... , stand for column vectors in the n-dimensional Euclidian space ℝn unless explicitly stated otherwise. The i-th component or element of a vector x is denoted by x i . The superscripts usually represent different vectors, for example, x k,k ∈ K where K is a set of indices. In general the columns of an m x n matrix A (or A m×n ) are denoted by a 1,a 2 ⋯,a n, while the rows by A 1, A 2, ..., A m or {A}i, i = 1, ⋯ , m. The entry in row i and column j of a matrix A is denoted by a ij . g(x)is a column vector-valued function with scalar-valued functions g 1 (x), g 2 (x), ... ,g m (x) as its components. In the following chapters, we sometimes write f k,g k as abbreviations for f (x k),g(x k).
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© 2000 Springer Science+Business Media Dordrecht
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Zhang, XS. (2000). Preliminaries. In: Neural Networks in Optimization. Nonconvex Optimization and Its Applications, vol 46. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3167-5_1
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DOI: https://doi.org/10.1007/978-1-4757-3167-5_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4836-6
Online ISBN: 978-1-4757-3167-5
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