Preliminaries

  • Xiang-Sun Zhang
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 46)

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 n 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 ,kK 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 ).

Keywords

Equilibrium Point Convex Function Lyapunov Function Travel Salesman Problem Hamilton Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Xiang-Sun Zhang
    • 1
  1. 1.Academy of Mathematics and Systems, Institute of Applied MathematicsChinese Academy of SciencesChina

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