A Unifying Framework for Global Optimization: From Theory to Formalization

📝 Original Info

• Title: A Unifying Framework for Global Optimization: From Theory to Formalization
• ArXiv ID: 2508.20671
• Date: 2025-08-28
• Authors: ** (논문에 명시된 저자 정보가 제공되지 않았습니다.) **

📝 Abstract

We introduce an abstract measure___theoretic framework that serves as a tool to rigorously study stochastic iterative global optimization algorithms as a unified class. The framework is formulated in terms of probability kernels, which, via the Ionescu--Tulcea theorem, induce probability measures on the space of sequences of algorithm iterations, endowed with two intuitive properties. This framework answers the need for a general, implementation___independent formalism in the analysis of such algorithms, providing a starting point for formalizing general results in proof-assistants. To illustrate the relevance of our tool, we show that common algorithms fit naturally in the framework, and we also use it to give a rigorous proof of a general consistency theorem for stochastic iterative global optimization algorithms (Proposition 3 of (Malherbe, et al., 2017). This proof and the entire framework are formalized in the Lean proof assistant. This formalization both ensures the correctness of the definitions and proofs, and provides a basis for future machine-assisted formalizations in the field.

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