Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian for C2-no...

This paper presents a method based on nonlinear programming for short term scheduling of hydro power system. The proposed algorithm is based on the solution of an augmented lagrangian function of the scheduling problem using conjugate gradient method. The water transportation delay between cascaded reservoirs is considered. Results concerning this method are compared with those achieved from su...

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton li...

We consider the global and local convergence properties of a class of Lagrangian barrier methods for solving nonlinear programming problems. In such methods, simple bound constraints may be treated separately from more general constraints. The objective and general constraint functions are combined in a Lagrangian barrier function. A sequence of such functions are approximately minimized within...

In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that the penalty parameter can be taken appropriately, so a single minimization of the augmented Lagrangian recovers a solution of the original problem. This leads to reformulations of NSDP problems into unconstrained nonlin...

To improve thequalityofdecisionmaking in theprocessoperations, it is essential to implement integrated planning and scheduling optimization. Major challenge for the integration lies in that the corresponding optimization problem is generally hard to solve because of the intractable model size. In this paper, ccepted 18 November 2009 vailable online 24 November 2009 eywords: lanning and scheduli...

In this paper, an algorithm for sparse learning via Maximum Margin Matrix Factorization(MMMF) is proposed. The algorithm is based on L1 penality and Alternating Direction Method of Multipliers. It shows that with sparse factors, sparse factors method can obtain result as good as dense factors.

This paper is devoted to the design of a decentralized optimal batch LQ state observer for state estimation of large-scale interconnected systems, well suited for implementation on a sensor network. The here-proposed approach relies on both the use of an augmented Lagrangian formulation and a price-decomposition-coordination algorithm. The state estimation of an openchannel hydraulic system ill...

The Signorini problem describes the contact of a linearly elastic body with a rigid frictionless foundation. It is transformed into a saddle point problem of some augmented Lagrangian functional and then discretized by nite element methods. Optimal error estimates are obtained for general smooth domains which are not necessarily convex. The key ingredient in the analysis is a discrete inf-sup c...