MATLAB Active Set Algorithm for Convex Quadratic Programming

This article presents a highly practical algorithm - the MATLAB active set method for convex quadratic programming. The algorithm solves convex quadratic programming problems through a systematic sequence of steps including problem modeling, constraint identification, and iterative solution procedures. From an implementation perspective, the algorithm typically involves: - Initializing a feasible starting point and corresponding active set - Solving equality-constrained quadratic subproblems using MATLAB's quadprog function or direct matrix operations - Iteratively updating the active set based on Lagrange multiplier signs and constraint violations - Handling both equality and inequality constraints through efficient matrix computations The key advantage lies in its efficient handling of constraints by focusing only on binding constraints at each iteration, significantly reducing computational complexity. This implementation can dramatically improve solving efficiency for convex quadratic programming problems. I recommend adding this algorithm to your collection for future optimization tasks, as it provides a robust foundation for constrained optimization problems commonly encountered in engineering and financial applications.