We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modifi...

Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that does not correspond to the fixed grid locations used to forecast the prognostic flow variables. A new method is presented for assimilating Lagrangian data into models of the ocean that...

Laser plasma is modeled by Lagrangian hydrodynamical equations including heat conductivity and laser absorption. The hyperbolic part of the model is treated by Arbitrary Lagrangian Eulerian (ALE) method which avoids moving mesh distortion and parabolic heat conductivity part is treated by splitting and mimetic method. High velocity laser accelerated disc impact problems for which standard Lagra...

We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a lo...