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A Derivative-free Two Level Random Search Method for Unconstrained Optimization (Paperback, 1st ed. 2021)
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A Derivative-free Two Level Random Search Method for Unconstrained Optimization (Paperback, 1st ed. 2021)
Series: SpringerBriefs in Optimization
Expected to ship within 10 - 15 working days
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The book is intended for graduate students and researchers in
mathematics, computer science, and operational research. The book
presents a new derivative-free optimization method/algorithm based
on randomly generated trial points in specified domains and where
the best ones are selected at each iteration by using a number of
rules. This method is different from many other well established
methods presented in the literature and proves to be competitive
for solving many unconstrained optimization problems with different
structures and complexities, with a relative large number of
variables. Intensive numerical experiments with 140 unconstrained
optimization problems, with up to 500 variables, have shown that
this approach is efficient and robust. Structured into 4 chapters,
Chapter 1 is introductory. Chapter 2 is dedicated to presenting a
two level derivative-free random search method for unconstrained
optimization. It is assumed that the minimizing function is
continuous, lower bounded and its minimum value is known. Chapter 3
proves the convergence of the algorithm. In Chapter 4, the
numerical performances of the algorithm are shown for solving 140
unconstrained optimization problems, out of which 16 are real
applications. This shows that the optimization process has two
phases: the reduction phase and the stalling one. Finally, the
performances of the algorithm for solving a number of 30
large-scale unconstrained optimization problems up to 500 variables
are presented. These numerical results show that this approach
based on the two level random search method for unconstrained
optimization is able to solve a large diversity of problems with
different structures and complexities. There are a number of open
problems which refer to the following aspects: the selection of the
number of trial or the number of the local trial points, the
selection of the bounds of the domains where the trial points and
the local trial points are randomly generated and a criterion for
initiating the line search.
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