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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Search and Optimization in Topological Spaces
verfasst von : Alan J. Lockett
Erschienen in: General-Purpose Optimization Through Information Maximization
Verlag: Springer Berlin Heidelberg
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Probability theory is built on measurable spaces, typically finite-dimensional Euclidean space. But in order to analyze search and optimization processes, probability measures over sequences, functions, and other complex objects are needed. In many cases these spaces are not just infinite but infinite-dimensional; they can vary infinitely in infinitely many aspects. Finite analysis, and even real analysis, does not suffice to study such spaces. Functional analysis is required, which is presently built on the foundation of general topology to supply meaning for terms such as continuity and convergence.