Subdomain Separability in Global Optimization

TL;DR

This paper introduces a generalized concept of subdomain separability for differentiable functions in global optimization, enabling automatic verification and significant search space reduction to accelerate optimization algorithms.

Contribution

It extends the notion of separability to a broader class of functions and demonstrates how to use interval derivatives for automatic verification within a branch and bound framework.

Findings

Significant search space reduction expected in global optimization.

Automatic verification of structural separators using interval derivatives.

Applicability to differentiable computer programs.

Abstract

We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound method. The often significant search space reduction can be expected to yield an acceleration of any global optimization method. We show how to utilize interval derivatives calculated by adjoint algorithmic differentiation to examine the monotonicity of the objective with respect to so called structural separators and how to verify the latter automatically.