# A Unified Funnel Restoration SQP Algorithm

arXiv: https://arxiv.org/abs/2409.09208 · HTML: https://mlsanity.com/paper/2409.09208/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2024.

## Built on by (most cited first, 1 of 1)

- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)

## Abstract (arXiv)

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.