  This monograph is about discrete energy minimization for discrete graphical
models. It considers graphical models, or, more precisely, maximum a posteriori
inference for graphical models, purely as a combinatorial optimization problem.
Modeling, applications, probabilistic interpretations and many other aspects
are either ignored here or find their place in examples and remarks only. It
covers the integer linear programming formulation of the problem as well as its
linear programming, Lagrange and Lagrange decomposition-based relaxations. In
particular, it provides a detailed analysis of the polynomially solvable
acyclic and submodular problems, along with the corresponding exact
optimization methods. Major approximate methods, such as message passing and
graph cut techniques are also described and analyzed comprehensively. The
monograph can be useful for undergraduate and graduate students studying
optimization or graphical models, as well as for experts in optimization who
want to have a look into graphical models. To make the monograph suitable for
both categories of readers we explicitly separate the mathematical optimization
background chapters from those specific to graphical models.
