# A Method to Guarantee Local Convergence for Sequential Quadratic Programming with Poor Hessian Approximation

## TL;DR

This paper introduces a simple method to ensure local convergence of SQP algorithms even when using poor Hessian approximations, addressing practical computational challenges.

## Contribution

It proposes a novel approach that guarantees local convergence of SQP with low-quality Hessian approximations, which was not previously established.

## Key findings

- The method guarantees local convergence despite poor Hessian approximations.
- Numerical example demonstrates the effectiveness of the proposed approach.

## Abstract

Sequential Quadratic Programming (SQP) is a powerful class of algorithms for solving nonlinear optimization problems. Local convergence of SQP algorithms is guaranteed when the Hessian approximation used in each Quadratic Programming subproblem is close to the true Hessian. However, a good Hessian approximation can be expensive to compute. Low cost Hessian approximations only guarantee local convergence under some assumptions, which are not always satisfied in practice. To address this problem, this paper proposes a simple method to guarantee local convergence for SQP with poor Hessian approximation. The effectiveness of the proposed algorithm is demonstrated in a numerical example.