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In the intervening years since this book was published in 1981, the
field of optimization has been exceptionally lively. This fertility
has involved not only progress in theory, but also faster numerical
algorithms and extensions into unexpected or previously unknown
areas such as semidefinite programming. Despite these changes, many
of the important principles and much of the intuition can be found
in this Classics version of Practical Optimization. This book
provides model algorithms and pseudocode, useful tools for users
who prefer to write their own code as well as for those who want to
understand externally provided code. It presents algorithms in a
step-by-step format, revealing the overall structure of the
underlying procedures and thereby allowing a high-level perspective
on the fundamental differences. And it contains a wealth of
techniques and strategies that are well suited for optimization in
the twenty-first century, and particularly in the now-flourishing
fields of data science, "big data," and machine learning. Practical
Optimization is appropriate for advanced undergraduates, graduate
students, and researchers interested in methods for solving
optimization problems.
Numerical Linear Algebra and Optimization covers the fundamentals
of closely related topics: linear systems (linear equations and
least-squares) and linear programming (optimizing a linear function
subject to linear constraints). For each problem class, stable and
efficient numerical algorithms intended for a finite-precision
environment are derived and analyzed. In 1991, when the book first
appeared, these topics were rarely taught with a unified
perspective, and, somewhat surprisingly, this remains true almost
30 years later. As a result, some of the material in this book can
be difficult to find elsewhere-in particular, techniques for
updating the LU factorization, descriptions of the simplex method
applied to all-inequality form, and the analysis of what happens
when using an approximate inverse to solve Ax=b. This book is
appropriate for students who want to learn about numerical
techniques for solving linear systems and/or linear programming
using the simplex method.
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