Mathematical Preliminaries

  • Kiyotaka Shimizu
  • Yo Ishizuka
  • Jonathan F. Bard

Abstract

This subsection is devoted to introducing notation and definitions that are used throughout the book. Constants, variables and functions are boldfaced to show that they are vectors or vector-valued. Vectors are column oriented unless otherwise specified. For two vectors
$$ x = \left( {\begin{array}{*{20}{c}} {{x_1}} \\ \vdots \\ {{x_n}} \end{array}} \right),{\text{ }}y = \left( {\begin{array}{*{20}{c}} {{y_1}} \\ \vdots \\ {{y_n}} \end{array}} \right)$$
the inner product,\( \Sigma _{i = 1}^n{x_i}{y_i} \), of x and y is denoted by x T y. Superscript T stands for the transposition. When x is a row vector, we write the inner product as xy.

Keywords

Convex Function Directional Derivative Inequality System Mathematical Preliminary Alternative Theorem 
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 New York 1997

Authors and Affiliations

  • Kiyotaka Shimizu
    • 1
  • Yo Ishizuka
    • 2
  • Jonathan F. Bard
    • 3
  1. 1.Keio UniversityYokohamaJapan
  2. 2.Sophia UniversityTokyoJapan
  3. 3.The University of TexasAustinUSA

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