MATLAB Programming Example of Sequential Quadratic Programming (SQP) Algorithm

This article presents a MATLAB programming example of the Sequential Quadratic Programming (SQP) algorithm, complete with detailed explanations including a Quadratic Programming (QP) subroutine implementation. We explore how to utilize the SQP algorithm for solving optimization problems and provide practical techniques and recommendations to enhance its real-world application. The implementation covers MATLAB-specific programming approaches, demonstrating how to structure the main SQP routine and subordinate QP solver, with emphasis on handling constraint gradients and Hessian matrix approximations. We detail parameter adjustment strategies for convergence control, including tolerance settings and maximum iteration limits. Additionally, we examine code optimization practices such as efficient Jacobian calculation and warm-start techniques for QP subproblems. The article concludes with practical examples illustrating SQP's application scenarios and advantages in nonlinear constrained optimization, highlighting its convergence properties and implementation efficiency through comparative performance analysis.