Chapter 8 (Sections 8.2 and 8.3); Chapter 9 (Section 9.4); Chapter 10 (Section
10.6).
This volume can also be used as a basic text for an introductory course on any
of the subjects covered here. In this case, additional sources of reference should
be searched, including conference proceedings. The most recent advances and
variations of the algorithms presented could be added so as to complement the
contents presented here.
Concerning Appendix B, dedicated to the Theoretical Background for the
book, the required background for each chapter is as follows:
Chapter 3: Section B.2.1, B.2.4, B.4.1, and B.4.4.
Chapter 4: Sections B.1, B.4.2, B.4.3, B.4.4 and B.4.5.
Chapter 5: Sections B.4.1, B.4.4 and B.4.5.
Chapter 6: Sections B.4.1, B.4.4 and B.4.5.
Chapter 7: Sections B.1, B.4.3, B.4.5 and B.4.6.
Chapter 8: Part I of the book, with emphasis on Chapters 3 and 4.
Chapter 9: Section B.3.
Chapter 10: Sections B.1, B.2, B.3 and B.4.7.
Also, take the attention of the students for Appendices A and C, written as a
general glossary to the terminology and a guide to the literature, respectively.
Notation
While writing such a wide-ranging volume, some major concerns are uniformity
and notation. Special care was taken to provide a concise and uniform notation
to the text. The readers are invited to go through this Notation section before
commencing reading the book. Appendix B complements this notation by pro-
viding a brief review of the theoretical background necessary for a thorough
understanding of the book using the standard notation style of the whole text.
o Scalars are denoted by italic lowercase Roman letters: e.g., a, b, x, y, z.
o Vectors are denoted by boldface lowercase Roman letters: e.g., x, y, z.
o Matrices are denoted by boldface uppercase Roman letters: e.g., X, Y, Z.
o n-dimensional Euclidean space: ℜ
n
.
o Matrix with n rows and m columns, and real-valued entries: X ∈ ℜ
n×m
.
o Vector with n entries (always assumed to be a column vector, unless oth-
erwise specified): x ∈ ℜ
n
.
o The transpose of a vector or matrix is denoted by an italic uppercase letter
‘T’: e.g., x
T
, X
T
.
o Problem of minimizing function f(x) over choices of x that lie in the set of
feasible solutions: min f(x).
o Problem of maximizing function f(x) over choices of x that lie in the set
of feasible solutions: max f(x).
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