A trust-region funnel algorithm for gray-box optimization

TL;DR

This paper introduces a novel trust-region funnel algorithm for gray-box optimization that simplifies existing methods, maintains convergence guarantees, and demonstrates improved performance in benchmarks.

Contribution

It proposes a new TR funnel algorithm replacing filter criteria with a funnel, supported by convergence proof and open-source implementation in Pyomo.

Findings

Achieves comparable or better performance than classical TR filter methods.

Supports multiple reduced model forms and globalization strategies.

Provides a simpler, effective approach for gray-box optimization.

Abstract

Gray-box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black-box models lacking analytic derivatives, remains a challenge. Trust-region (TR) methods provide a robust framework for gray-box problems through local reduced models (RMs) for black-box components, but they are complex and require extensive parameter tuning. Motivated by recent advances in funnel-based convergence theory for nonlinear optimization, we propose a novel TR funnel algorithm for gray-box optimization, replacing the filter acceptance criterion with a uni-dimensional funnel, maintaining a monotonically decreasing upper bound on approximation error of local black-box RMs. A global convergence proof to a first-order critical point is established. The algorithm, implemented open-source in Pyomo, supports multiple RM forms and globalization strategies (filter or funnel). Benchmark tests show the TR funnel algorithm achieves comparable and often improved performance relative to the classical TR filter method, thus providing a simpler, effective alternative for gray-box optimization.