A block active set algorithm for large-scalequadratic programming with box constraints

TL;DR: An algorithm for computing a stationary point of a quadratic program with box constraints (BQP) is proposed and it is shown that the algorithm terminates after a finite number of iterations, if at least one iterate is sufficiently close to a stationary Point which satisfies a certain sufficient optimality condition.

Abstract: An algorithm for computing a stationary point of a quadratic program with box constraints(BQP) is proposed. Each iteration of this procedure comprises a guessing strategy whichforecasts the active bounds at a stationary point, the determination of a descent direction bymeans of solving a reduced strictly convex quadratic program with box constraints and anexact line search. Global convergence is established in the sense that every accumulationpoint is stationary. Moreover, it is shown that the algorithm terminates after a finite numberof iterations, if at least one iterate is sufficiently close to a stationary point which satisfiesa certain sufficient optimality condition. The algorithm can be easily implemented for sparselarge-scale BQPs. Furthermore, it simplifies for concave BQPs, as it is not required to solvestrictly convex quadratic programs in this case. Computational experience with large-scaleBQPs is included and shows the appropriateness of this type of methodology.