The same idea in Subsection 3.3 can be extended to combine dual method and augmented Lagrangian projection method in Subsection 3.2, and this will lead to the dual augmented Lagrangian projection method.
The fast split Bregman method [24, 25], dual method [26], and augmented Lagrangian method [28] proposed for TV model for image restoration have been successfully extended to the Chan-Vese model under VLFM framework [20, 38], but they cannot be directly applied to Chan-Vese model under VLSM framework due to the complex constraint |∇ϕ| = 1.
For example, novel split Bregman algorithm [24, 25], dual method [26, 27], and augmented Lagrangian method [21, 22, 28], and these fast algorithms all avoid computing complex curvature associated with TV regularizer term.
The data were analyzed using a three-way multivariate curve resolution alternating least squares method (MCR-ALS) and augmented matrices.
Optimization process is performed using three scalarization approaches, namely weighted sum method, weighted Tchebycheff and augmented weighted Tchebycheff.
Alternating direction method of multipliers (ADMM) is another optimization method which uses properties of dual decomposition and augmented Lagrangian methods simultaneously (Boyd & Vandenberghe 2004).
The framework is modeled as a mixed integer nonlinear programming (MINLP) problem and the outer-approximation method with equality relaxation and augmented penalty (OA/ER/AP) is employed to solve it.
Detail contact algorithm based on sequential quadratic programming (SQP) and augmented Lagrange method is introduced and applied on complex contact friction problem successfully.
Gathering the information for such a case and presenting it in a clinical image will serve for physicians to be aware of this cutaneous variant, demonstrate alternative treatment methods of CL, and augment the body of knowledge in this field.
Rice crop data were analyzed using the ordinary least square method and the augmented Dickey Fuller test.
