Global Search Based on Efficient Diagonal Partitions and a set of Lipschitz Constants

TL;DR

This paper introduces a new global optimization algorithm for multidimensional black-box functions with unknown Lipschitz constants, combining diagonal partitioning and adaptive Lipschitz constant estimation, demonstrating strong performance on extensive tests.

Contribution

The paper presents a novel global optimization method that adaptively estimates Lipschitz constants and employs diagonal partitions, improving efficiency over existing algorithms.

Findings

Algorithm outperforms existing methods on over 1600 test functions.

Adaptive Lipschitz constant selection enhances optimization efficiency.

Diagonal partitioning effectively balances local and global search.

Abstract

In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants is chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance.