Simplicial Global Optimization is centered on deterministic covering
methods partitioning feasible region by simplices. This book looks into
the advantages of simplicial partitioning in global optimization through
applications where the search space may be significantly reduced while
taking into account symmetries of the objective function by setting
linear inequality constraints that are managed by initial partitioning.
The authors provide an extensive experimental investigation and
illustrates the impact of various bounds, types of subdivision,
strategies of candidate selection on the performance of algorithms. A
comparison of various Lipschitz bounds over simplices and an extension
of Lipschitz global optimization with-out the Lipschitz constant to the
case of simplicial partitioning is also depicted in this text.
Applications benefiting from simplicial partitioning are examined in
detail such as nonlinear least squares regression and pile placement
optimization in grillage-type foundations. Researchers and engineers
will benefit from simplicial partitioning algorithms such as Lipschitz
branch and bound, Lipschitz optimization without the Lipschitz constant,
heuristic partitioning presented. This book will leave readers inspired
to develop simplicial versions of other algorithms for global
optimization and even use other non-rectangular partitions for special
applications.
