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4101. Advanced numerical methods for Lipschitz global optimization

Invited abstract in session MC-41: Stochastic and Deterministic Global Optimization, stream Stochastic and Deterministic Global Optimization.

Monday, 12:30-14:00
Room: 97 (building: 306)

Authors (first author is the speaker)

1. Dmitri Kvasov
DIMES, University of Calabria
2. Yaroslav Sergeyev
DIMES, University of Calabria

Abstract

Decision-making problems defined as global optimization problems of an objective function subject to a set of constraints arise in various application fields. The objective function and constraints can be black box and difficult to evaluate functions with unknown analytical representations. This means that there are black boxes associated with the functions which, given the values of the input parameters, return the values of the corresponding functions and the optimizer knows nothing about how these values are obtained. Therefore, one of the main goals in this context is to develop fast global optimization algorithms that produce reasonably good solutions with a limited number of function evaluations. We will discuss various deterministic approaches based on the Lipschitz continuity assumption to construct efficient and reliable numerical methods to solve the mentioned problems. Among these, the divide-the-best scheme for developing and studying numerical methods in a unitary way, the index scheme for managing non-convex constraints and the local tuning on the function’s behaviour will be examined in particular (see https://doi.org/10.1007/978-3-030-54621-2_764-1). Some recently proposed high-precision techniques (including the infinite computing paradigm https://www.theinfinitycomputer.com) will also be considered.

This work was partially supported by the Italian INdAM GNCS Project 2023, number CUP_E53C22001930001.

Keywords

Status: accepted

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