Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing Huibin Chang and Xue-Cheng Tai2,∗ 1 School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387; Department of Mathematics, East China Normal University, Shanghai 200241, China. 2 Department of Mathematics, University of Bergen, Johaness Brunsgate 12, Berg...

In this paper, we study the semidefinite inverse eigenvalue problem of reconstructing a real n-by-n matrix C such that it is nearest to the original pre-estimated real n-by-n matrix Co in the Frobenius norm and satisfies the measured partial eigendata, where the required matrix C should preserve the symmetry, positive semidefiniteness, and the prescribed entries of the preestimated matrix Co. W...

[1] M. Gallieri, J. M. Maciejowski “lasso MPC: Smart Regulation of OverActuated Systems”, to appear in ACC 2012. [2] M. Annergren, A. Hansson, B. Wahlberg “An ADMM Algorithm for Solving l1 Regularized MPC”, submitted. [3] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers”, Foundations and Tr...

Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and...

This note shows the O(1/t) convergence rate of Eckstein and Bertsekas’s generalized alternating direction method of multipliers in the context of convex minimization with linear constraints.

We compare three different time discretization schemes in combination with an augmented Lagrangian method to simulate the motion of an inextensible beam. The resulting saddle-point problem is solved with an Uzawa-DouglasRachford algorithm. The three schemes are tested on a benchmark with an analytical solution and on a more challenging application. We found that in order to obtain optimal conve...

This User’s Guide describes the functionality and basic usage of the Matlab package TVAL3 for total variation minimization. The main algorithm used in TVAL3 is briefly introduced in the appendix.

The paper focuses on the convergence rate of the augmented Lagrangian method for nonlinear second-order cone optimization problems. Under a set of assumptions of sufficient conditions, including the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second order sufficient condition, we first study some properties of the augmented Lagrangian and then ...