We propose augmented Lagrangian methods to solve state and control constrained optimal control problems. The approachis based on the Lagrangianformulationof nonsmoothconvex optimization in Hilbert spaces developed in 6]. We investigate a linear optimal control problem with a boundary control function as in 1]. Both the equation and the constraints are augmented. The proposed methods are general...

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augm...

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to bot...

Article history: Received 9 March 2012 Available online 4 October 2012 Communicated by G. Borgefors

We design inexact proximal augmented Lagrangian based decomposition methods for convex composite programming problems with dual block-angular structures. Our are particularly well suited quadratic arising from stochastic models. The algorithmic framework is on the application of abstract ADMM developed in [Chen, Sun, Toh, Math. Prog. 161:237–270] to target problem, as recently symmetric Gauss-S...

In our earlier work [4], a dual iterative substructuring method for two dimensional problems was proposed, which is a variant of the FETI-DP method. The proposed method imposes continuity on the interface by not only the pointwise matching condition but also uses a penalty term which measures the jump across the interface. For a large penalization parameter, it was proven that the condition num...

We consider the global convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In the proposed method, linear constraints are treated separately from more general constraints. Thus only the latter are combined with the objective function in an augmented Lagrangian. The subproblem then consists of (approximately) minimizing this augmented Lag...