An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization

Abstract

Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure. The algorithm effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration. We establish convergence for this algorithm, and apply it to solving problems in image reconstruction with total variation regularization. We present numerical results showing that the resulting solver, called TVAL3, is competitive with, and often outperforms, other state-of-the-art solvers in the field.

Document Details

• Document Type: Technical Report
• Publication Date: Aug 17, 2012
• Accession Number: ADA580738

Entities

People

• Chengbo Li
• Hong Jiang
• Wotao Yin
• Yin Zhang

Organizations

• Rice University

Tags

Communities of Interest

• Sensors

DTIC Thesaurus Topics

• Accuracy
• Algorithms
• Applied Mathematics
• Compressed Sensing
• Convergence
• Data Acquisition
• Gaussian Noise
• Image Processing
• Image Reconstruction
• Iterations
• Lagrangian Functions
• Mathematics
• Measurement
• Observation
• Optimization
• Sampling

Readers

• Operations Research