Multiplier and gradient methods

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075

Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

Boyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,677

Variational Mode Decomposition

Dragomiretskiy, K., & Zosso, D. (2014) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2288675 · Cited by 9,184

Numerical solution of saddle point problems

Benzi, M., Golub, G. H., & Liesen, J. (2005) · Acta Numerica · doi:10.1017/s0962492904000212 · Cited by 2,300

Fast Image Recovery Using Variable Splitting and Constrained Optimization

Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2047910 · Cited by 1,223

Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing

Yang, J., & Zhang, Y. (2011) · SIAM Journal on Scientific Computing · doi:10.1137/090777761 · Cited by 1,201

An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems

Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2011) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2076294 · Cited by 938

A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds

Conn, A. R., Gould, N. I. M., & Toint, P. (1991) · SIAM Journal on Numerical Analysis · doi:10.1137/0728030 · Cited by 873

A mixed formulation for frictional contact problems prone to Newton like solution methods

Alart, P., & Curnier, A. (1991) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(91)90022-x · Cited by 758

An efficient augmented Lagrangian method with applications to total variation minimization

Li, C., Yin, W., Jiang, H., & Zhang, Y. (2013) · Computational Optimization and Applications · doi:10.1007/s10589-013-9576-1 · Cited by 656

Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models

Wu, C., & Tai, X.-C. (2010) · SIAM Journal on Imaging Sciences · doi:10.1137/090767558 · Cited by 615

BM3D Frames and Variational Image Deblurring

Danielyan, A., Katkovnik, V., & Egiazarian, K. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2176954 · Cited by 611

Modeling mutual context of object and human pose in human-object interaction activities

Yao, B., & Fei-Fei, L. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5540235 · Cited by 573

Convex Optimization Theory

(2025) · Portfolio Optimization · doi:10.1017/9781009428095.021 · Cited by 553

Mean‐Variance Versus Direct Utility Maximization

KROLL, Y., LEVY, H., & MARKOWITZ, H. M. (1984) · The Journal of Finance · doi:10.1111/j.1540-6261.1984.tb03859.x · Cited by 527

A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration

Zhang, X., Burger, M., & Osher, S. (2011) · Journal of Scientific Computing · doi:10.1007/s10915-010-9408-8 · Cited by 419

A control perspective for centralized and distributed convex optimization

Wang, J., & Elia, N. (2011) · IEEE Conference on Decision and Control and European Control Conference · doi:10.1109/cdc.2011.6161503 · Cited by 398

Multiplier methods: A survey

Bertsekas, D. P. (1976) · Automatica · doi:10.1016/0005-1098(76)90077-7 · Cited by 347

Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2045029 · Cited by 334

Accelerated Attributed Network Embedding

Huang, X., Li, J., & Hu, X. (2017) · Proceedings of the 2017 SIAM International Conference on Data Mining · doi:10.1137/1.9781611974973.71 · Cited by 311

Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization—Part I: Algorithms and Convergence Analysis

Shi, Q., & Hong, M. (2020) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2020.3001906 · Cited by 283

Non-ferrous metals price forecasting based on variational mode decomposition and LSTM network

Liu, Y., Yang, C., Huang, K., & Gui, W. (2020) · Knowledge-Based Systems · doi:10.1016/j.knosys.2019.105006 · Cited by 253

Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms

Jakovetic, D., Moura, J. M. F., & Xavier, J. (2015) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2363299 · Cited by 123

PETSc/TAO Users Manual (Rev. 3.19)

Argonne National Laboratory (ANL), A., Balay, S., USDOE Office of Science (SC), A. S. C. R. (., Abhyankar, S., Adams, M., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, E., et al. (2023) · doi:10.2172/1968587 · Cited by 67

Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

Fioretto, F., Mak, T. W. K., & Van Hentenryck, P. (2020) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v34i01.5403 · Cited by 29

Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer

Yonaga, K., Miyama, M. J., & Ohzeki, M. (2020) · arXiv · doi:10.48550/arxiv.2012.06119 · Cited by 10