The role of the multipliers in the multiplier method

The paper studies the role of the multipliers when the multiplier method is applied as a computational technique for minimizing penalized cost functionals for optimal control problems characterized by linear systems and integral quadratic costs.Theauthor would like to gratefully thank two anonymous referees for many helpful suggestions which led to a major improvement in both the quality and clarity of the paper, and to Professor Angelo Miele for his encouragement.