MATLAB Implementation of SQP Algorithm with Subroutines and Main Problem Integration

The MATLAB implementation of the SQP (Sequential Quadratic Programming) algorithm requires systematic development of multiple interconnected components. The core implementation involves creating specialized subroutines for handling quadratic programming subproblems, merit function evaluation, and Hessian approximation techniques such as BFGS updates. The main algorithm structure typically implements an iterative optimization loop that sequentially solves quadratic approximations of the original nonlinear constrained problem. Key implementation aspects include developing functions for constraint handling using active-set methods or interior-point approaches, gradient calculation through finite differences or automatic differentiation, and line search procedures with Armijo conditions. The integration framework ensures proper data flow between subroutines and the main optimization driver, maintaining consistency in variable management and convergence criteria checking. To achieve optimal performance, the implementation should incorporate rigorous validation tests including benchmark problem comparisons, sensitivity analysis for parameter tuning, and convergence monitoring through residual norms and constraint satisfaction metrics. The code structure should follow modular programming principles with clear interface definitions between components, enabling easy maintenance and potential extension to large-scale optimization problems. Advanced implementation techniques may include sparse matrix handling for efficiency, globalization strategies for robust convergence, and adaptive tolerance adjustment mechanisms.