论文信息 - On the method of multipliers for convex programming

On the method of multipliers for convex programming

It is known that the method of multipliers for constrained minimization can be viewed as a fixed stepsize gradient method for solving a certain, dual problem. In this short paper it is shown that for convex programming problems the method converges globally for a wide range of possible stepsizes. This fact is proved for both cases where unconstrained minimization is exact and approximate. The results provide the basis for considering modifications of the basic stepsize of the method of multipliers which are aimed at acceleration of its speed of convergence. A few such modifications are discussed and some computational results are presented relating to a problem in optimal control.

D. Bertsekas

[1] M. Powell. A method for nonlinear constraints in minimization problems , 1969 .

[2] M. Hestenes. Multiplier and gradient methods , 1969 .

[3] D. Bertsekas,et al. A DESCENT NUMERICAL METHOD FOR OPTIMIZATION PROBLEMS WITH NONDIFFERENTIABLE COST FUNCTIONALS , 1973 .

[4] R. Rockafellar. The multiplier method of Hestenes and Powell applied to convex programming , 1973 .

[5] D. Bertsekas,et al. Multiplier methods for convex programming , 1973, CDC 1973.

[6] D. Bertsekas. Convergence rate of penalty and multiplier methods , 1973, CDC 1973.

[7] R. Tyrrell Rockafellar,et al. A dual approach to solving nonlinear programming problems by unconstrained optimization , 1973, Math. Program..

[8] D. Bertsekas,et al. Combined Primal–Dual and Penalty Methods for Convex Programming , 1976 .