Simplicial Global Optimization

1. Front Matter

   Pages i-x

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2. Simplicial Partitions in Global Optimization

   • Remigijus Paulavičius, Julius Žilinskas

   Pages 1-19

3. Lipschitz Optimization with Different Bounds over Simplices

   • Remigijus Paulavičius, Julius Žilinskas

   Pages 21-60

4. Simplicial Lipschitz Optimization Without Lipschitz Constant

   • Remigijus Paulavičius, Julius Žilinskas

   Pages 61-86

5. Applications of Global Optimization Benefiting from Simplicial Partitions

   • Remigijus Paulavičius, Julius Žilinskas

   Pages 87-106

6. Back Matter

   Pages 107-137

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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.

• Lipschitz optimization
• Simplicial partitions
• branch and bound
• heuristic partitioning
• nonlinear least squares regression
• potentially optimal simplex
• combinatorics

“This is an excellent book written by the well-known specialists in the field of global optimization. The book can be equally useful for beginners and experts in global optimization. An interested reader may even be inspired to develop simplicial versions of other global optimization algorithms. I am sure that this book is a very valuable addition to the literature on global optimization and will be very much appreciated by grateful readers.” (Anatoly Zhigljavsky, Journal of Global Optimization, Vol. 60, 2014)

• Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

  Remigijus Paulavičius, Julius Žilinskas

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