On the minimum of a conditioned Brownian bridge
Abstract
We study the law of the minimum of a Brownian bridge, conditioned to take specific values at specific points, and the law of the location of the minimum. They are used to compare some non-adaptive optimisation algorithms for black-box functions for which the Brownian bridge is an appropriate probabilistic model and only a few points can be sampled.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2015
- DOI:
- 10.48550/arXiv.1511.05735
- arXiv:
- arXiv:1511.05735
- Bibcode:
- 2015arXiv151105735A
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Probability;
- 90C26;
- 60J65;
- 65C05
- E-Print:
- Revised and expanded Section 5: Non-adaptive optimisation