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Algorithmic Principles of Mathematical Programming investigates the
mathematical structures and principles underlying the design of
efficient algorithms for optimization problems. Recent advances in
algorithmic theory have shown that the traditionally separate areas
of discrete optimization, linear programming, and nonlinear
optimization are closely linked. This book offers a comprehensive
introduction to the whole subject and leads the reader to the
frontiers of current research. The prerequisites to use the book
are very elementary. All the tools from numerical linear algebra
and calculus are fully reviewed and developed. Rather than
attempting to be encyclopedic, the book illustrates the important
basic techniques with typical problems. The focus is on efficient
algorithms with respect to practical usefulness. Algorithmic
complexity theory is presented with the goal of helping the reader
understand the concepts without having to become a theoretical
specialist. Further theory is outlined and supplemented with
pointers to the relevant literature.
Algorithmic Principles of Mathematical Programming investigates the
mathematical structures and principles underlying the design of
efficient algorithms for optimization problems. Recent advances in
algorithmic theory have shown that the traditionally separate areas
of discrete optimization, linear programming, and nonlinear
optimization are closely linked. This book offers a comprehensive
introduction to the whole subject and leads the reader to the
frontiers of current research. The prerequisites to use the book
are very elementary. All the tools from numerical linear algebra
and calculus are fully reviewed and developed. Rather than
attempting to be encyclopedic, the book illustrates the important
basic techniques with typical problems. The focus is on efficient
algorithms with respect to practical usefulness. Algorithmic
complexity theory is presented with the goal of helping the reader
understand the concepts without having to become a theoretical
specialist. Further theory is outlined and supplemented with
pointers to the relevant literature.
The book is equally suited for self-study for a motivated beginner
and for a comprehensive course on the principles of mathematical
programming within an applied mathematics or computer science
curriculum at advanced undergraduate or graduate level. The
presentation of the material is such that smaller modules on
discrete optimization, linear programming, and nonlinear
optimization can easily be extracted separately and used for
shorter specialized courses on these subjects.
What is a game? Classically, a game is perceived as something
played by human beings. Its mathematical analysis is
human-centered, explores the structures of particular games,
economic or social environments and tries to model supposedly
'rational' human behavior in search of appropriate 'winning
strategies'. This point of view places game theory into a very
special scientific corner where mathematics, economics and
psychology overlap and mingle.This book takes a novel approach to
the subject. Its focus is on mathematical models that apply to game
theory in particular but exhibit a universal character and thus
extend the scope of game theory considerably.This textbook
addresses anyone interested in a general game-theoretic view of the
world. The reader should have mathematical knowledge at the level
of a first course in real analysis and linear algebra. However,
possibly more specialized aspects are further elaborated and
pointers to relevant supplementary literature are given. Moreover,
many examples invite the reader to participate 'actively' when
going through the material. The scope of the book can be covered in
one course on Mathematical Game Theory at advanced undergraduate or
graduate level.
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