Cargando…
Deterministic global optimization : an introduction to the diagonal approach /
This book begins with a concentrated introduction into deterministic global optimization and moves forward to present new original results from the authors who are well known experts in the field. Multiextremal continuous problems that have an unknown structure with Lipschitz objective functions and...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer,
[2017]
|
| Colección: | SpringerBriefs in optimization.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 1 Lipschitz Global Optimization; 1.1 Problem Statement; 1.2 Lipschitz Condition and Its Geometric Interpretation; 1.3 Multidimensional Approaches; 2 One-Dimensional Algorithms and Their Acceleration; 2.1 One-Dimensional Lipschitz Global Optimization; 2.2 Geometric LGO Methods for Non-differentiable Functions; 2.3 Geometric LGO Methods for Differentiable Functions with the Lipschitz First Derivatives; 2.4 Acceleration Techniques Embedded in the Univariate Global Optimization; 2.5 Numerical Illustrations; 3 Diagonal Approach and Efficient Diagonal Partitions.
- 3.1 General Diagonal Scheme3.2 Analysis of Traditional Diagonal Partition Schemes; 3.3 Non-redundant Diagonal Partition Strategy; 4 Global Optimization Algorithms Based on the Non-redundant Partitions ; 4.1 Multiple Estimates of the Lipschitz Constant; 4.2 Derivative-Free Diagonal Method MultL; 4.2.1 Theoretical Background of MultL: Lower Bounds; 4.2.2 Theoretical Background of MultL: Finding Non-dominated Hyperintervals; 4.2.3 Description of the MultL Algorithm and its Convergence Analysis; 4.3 One-Point-Based Method MultK for Differentiable Problems.
- 4.3.1 Theoretical Background of MultK: Lower Bounds4.3.2 Theoretical Background of MultK: Non-dominated Hyperintervals; 4.3.3 Description of the MultK Algorithm and its Convergence Analysis; 4.4 Numerical Experiments with the MultL and MultK Methods; 4.5 A Case Study: Fitting a Sum of Dumped Sinusoids to a Series of Observations; 4.5.1 Examples Illustrating the Complexity of the Problem; 4.5.2 Derivatives and Simplifications of the Benchmark Objective Functions; 4.5.3 Numerical Examples and Simulation Study; Appendix References.