A Unified Funnel Restoration SQP Algorithm

TL;DR

This paper introduces a unified double-loop SQP algorithm with a funnel constraint approach for nonlinear optimization, implemented in the open-source Uno solver, demonstrating global convergence and extensive testing on benchmark problems.

Contribution

It presents a novel unified framework for nonlinear optimization solvers, incorporating a funnel-based SQP algorithm with proven global convergence, implemented in the open-source Uno platform.

Findings

Global convergence of the funnel SQP method is established.

Extensive testing shows effectiveness on CUTEst benchmark problems.

The framework unifies various nonlinear optimization techniques.

Abstract

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.