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Books > Science & Mathematics > Mathematics > Optimization
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Introduction to Continuous Optimization (Hardcover, 1st ed. 2021)
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Introduction to Continuous Optimization (Hardcover, 1st ed. 2021)
Series: Springer Optimization and Its Applications, 172
Expected to ship within 12 - 17 working days
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This self-contained monograph presents the reader with an
authoritative view of Continuous Optimization, an area of
mathematical optimization that has experienced major developments
during the past 40 years. The book contains results which have not
yet been covered in a systematic way as well as a summary of
results on NR theory and methods developed over the last several
decades. The readership is aimed to graduate students in applied
mathematics, computer science, economics, as well as researchers
working in optimization and those applying optimization methods for
solving real life problems. Sufficient exercises throughout provide
graduate students and instructors with practical utility in a
two-semester course in Continuous Optimization. The topical
coverage includes interior point methods, self-concordance theory
and related complexity issues, first and second order methods with
accelerated convergence, nonlinear rescaling (NR) theory and
exterior point methods, just to mention a few. The book contains a
unified approach to both interior and exterior point methods with
emphasis of the crucial duality role. One of the main achievements
of the book shows what makes the exterior point methods numerically
attractive and why. The book is composed in five parts. The first
part contains the basics of calculus, convex analysis, elements of
unconstrained optimization, as well as classical results of linear
and convex optimization. The second part contains the basics of
self-concordance theory and interior point methods, including
complexity results for LP, QP, and QP with quadratic constraint,
semidefinite and conic programming. In the third part, the NR and
Lagrangian transformation theories are considered and exterior
point methods are described. Three important problems in finding
equilibrium are considered in the fourth part. In the fifth and
final part of the book, several important applications arising in
economics, structural optimization, medicine, statistical learning
theory, and more, are detailed. Numerical results, obtained by
solving a number of real life and test problems, are also provided.
General
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