Sammendrag
The last 20 years gave rise to revolutionary
developments, both in computer technology and in
software and algorithm improvements . As a
consequence, Linear Optimization (LO) problems that
20 years ago required a computational time of one
month, can now be solved within 10 seconds.
The book address algorithmic improvements in Interior
Point Methods (IPMs) for LO, and introduce a new
class of kernel functions. The author derive many new
and tight estimates that greatly simplify the
analysis of IPMs. Ten specific kernel functions are
considered, and using the new estimates present a
complete complexity analysis for each of these
functions. Iterations bounds both for large- and
small-update methods for LO are derived. These
results are extended to semidefinite optimization and
linear complementarity problems. The book present an
easy implementations of IPMs algorithm, and
investigate the influence of the choice of the kernel
function on the computational behavior of the
algorithm for LO. An indispensable reference for
students and researchers in applied mathematics,
computer science, operations research, management
science and engineering.
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