Global optimization based on a statistical model and simplicial partitioning

By A. Žilinskas, Julius Zilinskas. 2002

42 citations recorded by the source corpus.

Abstract A statistical model for global optimization is constructed generalizing some properties of the Wiener process to the multidimensional case. An approach to the construction of global optimization algorithms is developed using the proposed statistical model. The convergence of an algorithm based on the constructed statistical model and simplicial partitioning is proved. Several versions of the algorithm are implemented and investigated.

Subfields: Computer Networks and Communications, Food Science, Mathematical Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Nando de Freitas
2. Eric Brochu
3. Vlad M. Cora
4. Ruben Martinez-Cantin
5. José A. Castellanos
6. Arnaud Doucet
7. Julius Zilinskas
8. Kirthevasan Kandasamy

In Food Science

1. Nando de Freitas
2. Eric Brochu
3. Vlad M. Cora
4. Julius Zilinskas

In Mathematical Physics

1. Nando de Freitas
2. Eric Brochu
3. Vlad M. Cora
4. Arnaud Doucet
5. Julius Zilinskas

Citations in the corpus

• Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, neutral): “There exist several early consistency proofs for Gaussian process based Bayesian optimization algorithms, in the onedimensional setting [102] and one for a simplification of the algorithm using simplicial partitioning in higher dimensions [164].”
• A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, methodology): “There exist several consistency proofs for this algorithm in the one-dimensional setting [Locatelli, 1997] and one for a simplification of the algorithm using simplicial partitioning in higher dimensions [Žilinskas and Žilinskas, 2002].”
• Branch and bound with simplicial partitions for global optimization (2008, methodology): “Statistical models [15] or heuristic estimates [11, 17] may be used to evaluate sub-regions.”
• A Bayesian exploration-exploitation approach for optimal online sensing and planning with a visually guided mobile robot (2009, methodology): “…by the highest infill in the top plot produces the GP fit in the plot shown below. convergence proofs for a simplification of the algorithm using simplicial partitioning in higher dimensions [Zilinskas and Zilinskas (2002)] and, more recently, for GPs with Matern kernels in Vazquez and Bect (2008).”