Global and Adaptive Scaling in a Separable Augmented Lagrangian Algorithm
نویسندگان
چکیده
Abstract. In this paper, we analyze the numerical behaviour of a separable Augmented Lagrangian algorithm with multiple scaling parameters, different parameters associated with each dualized coupling constraint as well as with each subproblem. We show that an optimal superlinear rate of convergence can be theoretically attained in the twice differentiable case and propose an adaptive scaling strategy with the same ideal convergence properties. Numerical tests performed on quadratic programs confirm that Adaptive Global Scaling subsumes former scaling strategies with one or many parameters.
منابع مشابه
An augmented Lagrangian affine scaling method for nonlinear programming
In this paper, we propose an Augmented Lagrangian Affine Scaling (ALAS) algorithm for general nonlinear programming, for which a quadratic approximation to the augmented Lagrangian is minimized at each iteration. Different from the classical sequential quadratic programming (SQP), the linearization of nonlinear constraints is put into the penalty term of this quadratic approximation, which resu...
متن کاملAugmented Lagrangians with possible infeasibility and finite termination for global nonlinear programming
In a recent paper, Birgin, Floudas and Mart́ınez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the αBB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On...
متن کاملGlobal Nonlinear Programming with possible infeasibility and finite termination
In a recent paper, Birgin, Floudas and Mart́ınez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the αBB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On...
متن کاملSolving Environmental/Economic Power Dispatch Problem by a Trust Region Based Augmented Lagrangian Method
This paper proposes a Trust-Region Based Augmented Method (TRALM) to solve a combined Environmental and Economic Power Dispatch (EEPD) problem. The EEPD problem is a multi-objective problem with competing and non-commensurable objectives. The TRALM produces a set of non-dominated Pareto optimal solutions for the problem. Fuzzy set theory is employed to extract a compromise non-dominated sol...
متن کاملAdaptive Augmented Lagrangian Methods for Large-Scale Equality Constrained Optimization
We propose an augmented Lagrangian algorithm for solving large-scale equality constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the cor...
متن کامل