Implementing a unified solver for nonlinearly constrained optimization

TL;DR

This paper introduces Uno, a modular, unified solver framework for nonlinearly constrained optimization that combines key algorithmic strategies, enabling flexible, efficient, and comparable solver implementations with demonstrated competitive performance.

Contribution

The paper presents a unifying framework with eight building blocks for Lagrange-Newton methods and implements Uno, a flexible, modular solver that simplifies development and experimentation in nonlinear optimization.

Findings

Uno is highly competitive against state-of-the-art solvers.

The framework enables easy combination of optimization strategies.

Uno supports multiple programming interfaces and emerging optimization areas.

Abstract

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno's software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.