The augmented Lagrangian (AL) method provides a flexible and efficient framework for solving extended-space full-waveform inversion (FWI), constrained nonlinear optimization problem whereby we seek model parameters wavefields that minimize the data residuals satisfy wave-equation constraint. AL-based wavefield reconstruction inversion, also known as iteratively refined extends search space of F...

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadrat...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with ramp rate, emission and transmission constraints. The proposed ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian function. In ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty ...

We present a review of the classical proximal point method for nding zeroes of maximal monotone operators, and its application to augmented Lagrangian methods, including a rather complete convergence analysis. Next we discuss the generalized proximal point methods, either with Bregman distances or -divergences, which in turn give raise to a family of generalized augmented Lagrangians, as smooth...

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...

We propose a novel framework for fast regularization of matrix-valued images. The resulting algorithms allow a unified treatment for a broad set of matrix groups and manifolds. Using an augmented-Lagrangian technique, we formulate a fast and highly parallel algorithm for matrixvalued image regularization. We demonstrate the applicability of the framework for various problems, such as motion ana...

In this paper we study nonlinear Lagrangian functions for constrained optimization problems which are, in general, nonlinear with respect to the objective function. We establish an equivalence between two types of zero duality gap properties, which are described using augmented Lagrangian dual functions and nonlinear Lagrangian dual functions, respectively. Furthermore, we show the existence of...