Deterministic global optimization : an introduction to the diagonal approach / Yaroslav D. Sergeyev, Dmitri E. Kvasov.

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