caa a22 4500 463168887 CHVBK 20180406164807.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10957-007-9238-5 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9238-5 On the Surrogate Gradient Algorithm forLagrangian Relaxation [Elektronische Daten] [T. Sun, Q. Zhao, P. Luh] When applied to large-scale separable optimization problems, the recently developed surrogate subgradient method for Lagrangian relaxation (Zhao et al.: J.Optim. Theory Appl. 100, 699-712, 1999) does not need to solve optimally all the subproblems to update the multipliers, as the traditional subgradient method requires. Based on it, the penalty surrogate subgradient algorithm was further developed to address the homogenous solution issue (Guan et al.: J. Optim. Theory Appl. 113, 65-82, 2002; Zhai et al.: IEEE Trans. Power Syst. 17, 1250-1257, 2002). There were flaws in the proofs of Zhao et al., Guan et al., and Zhai et al.: for problems with inequality constraints, projection is necessary to keep the multipliers nonnegative; however, the effects of projection were not properly considered. This note corrects the flaw, completes the proofs, and asserts the correctness of the methods. Springer Science+Business Media, LLC, 2007 Lagrangian relaxation nationallicence Surrogate subgradient nationallicence Inequality constraints nationallicence Sun T. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut Zhao Q. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut Luh P. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/3(2007-06-01), 413-416 0022-3239 133:3<413 2007 133 10957 https://doi.org/10.1007/s10957-007-9238-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9238-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sun T. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 700 1- Zhao Q. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 700 1- Luh P. Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, 100084, Beijing, China aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/3(2007-06-01), 413-416 0022-3239 133:3<413 2007 133 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer