PhD Thesis
How to cite it
Oliver Schütze, "Set Oriented Methods for Global Optimization",
PhD thesis, University of Paderborn, Paderborn, Germany, 2004.
Abstract
The personal improvement is an inherent desire of every individual. Since
the beginning optimization has been a very atractive field in mathematics
though a thorough and beautiful theory was developed only in the 1950s when
computers became available. Both new generations of computers with rapidly
growing capacities and new problems arising from ever advancing applications,
call perpetually for new optimization methods. The scope of this thesis is
to give a contribution to that issue, to develop new techniques for the
solution of modern optimization problems. To be more precise, we propose
in this work numerous schemes for the numerical treatment os some global
optimization problems.
Most of the algorithms which are presented here are based on particular
set-oriented multi-level schemes. Using these subdivision techniques we
propose several adaptive algorithms for the location of zeros within a
predescribed compact domain (Chapters 3 and 4).
Furthermore, we address the problem of the location of the stability
regions of parameter dependent delay differential equations (Chapter 5).
The main part of this thesis consists of the numerical schemes for the
computation of the set of solutions for multi-objective optimization
problems (Chapter 6). One interesting result of this thesis are
set-oriented continuation-like methods for models where the objectives are
twice continuously differentiable. These algorithms can also be used for
the computation of general implicitly defined manifolds, even in higher
dimensional space. This allows for the efficient computation of
optimization models with equality constraints.
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This PhD thesis can be downloaded here.
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