DSDP5 swMATH ID: 4411 Software Authors: Steven J. Benson; Yinyu Ye Description: Algorithm 875: DSDP5–software for semidefinite programming. DSDP implements the dual-scaling algorithm for semidefinite programming. The source code for this interior-point algorithm, written entirely in ANSI C, is freely available under an open source license. The solver can be used as a subroutine library, as a function within the Matlab environment, or as an executable that reads and writes to data files. Initiated in 1997, DSDP has developed into an efficient and robust general-purpose solver for semidefinite programming. Its features include a convergence proof with polynomially bounded worst-case complexity, primal and dual feasible solutions when they exist, certificates of infeasibility when solutions do not exist, initial points that can be feasible or infeasible, relatively low memory requirements for an interior-point method, sparse and low-rank data structures, extensibility that allows applications to customize the solver and improve its performance, a subroutine library that enables it to be linked to larger applications, scalable performance for large problems on parallel architectures, and a well-documented interface and examples of its use. The package has been used in many applications and tested for efficiency, robustness, and ease of use. Homepage: http://dl.acm.org/citation.cfm?id=1356057 Keywords: semidefinite programming; low-rank factorization; maxcut problem; nonlinear programming; exact penalty functions Related Software: SDPT3; SeDuMi; SDPA; CSDP; YALMIP; Mosek; CVXOPT; GloptiPoly; SparsePOP; COL; SDPLIB; CVX; Benchmarks for Optimization Software; CVXPY; SparseMatrix; CHOMPACK; Biq Mac; Matlab; NEOS; GAMS Cited in: 30 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year An unconstrained minimization method for solving low-rank SDP relaxations of the maxcut problem. Zbl 1206.90114Grippo, Luigi; Palagi, Laura; Piccialli, Veronica 2011 all top 5 Cited by 64 Authors 4 Vandenberghe, Lieven 3 Gualandi, Stefano 2 Boyd, Stephen Poythress 2 Bugarin, Florian 2 Henrion, Didier 2 Maffioli, Francesco 1 Andersen, Martin S. 1 Atamtürk, Alper 1 Bao, Xiaowei 1 Bartoli, Adrien 1 Benson, Steven J. 1 Cifuentes, Diego 1 Corbineau, Pierre 1 Croci, Matteo 1 Dahl, Joachim 1 Diamond, Steven 1 Dieudonné, Anca 1 Falkeborn, Rikard 1 Fujisawa, Katsuki 1 Fukuda, Mituhiro 1 Galbiati, Giulia 1 Gally, Tristan M. 1 Genoulaz, Jérôme 1 Goddet, Etienne 1 Grippo, Luigi 1 Guichon, Jean-Michel 1 Hansson, Anders 1 Jiang, Xin 1 Kim, Seung-Jean 1 Kim, Sunyoung 1 Kleniati, Polyxeni-Margarita 1 Kojima, Masakazu 1 Lasserre, Jean-Bernard 1 Lee, Eva K. 1 Liu, Zhang 1 Löfberg, Johan 1 Magni, Claudio 1 Michailidis, George C. 1 Mittelmann, Hans Detlef 1 Monniaux, David P. 1 Nakata, Kazuhide 1 Nakata, Maho 1 Narayanan, Vishnu 1 Nie, Jiawang 1 Orteu, Jean-José 1 Palagi, Laura 1 Parpas, Panos 1 Parrilo, Pablo A. 1 Pfetsch, Marc E. 1 Piccialli, Veronica 1 Retiere, Nicolas 1 Rustem, Berc 1 Sahinidis, Nikolaos V. 1 Sentenac, Thierry 1 Singhal, Harsh 1 Stojanović, Vojislav 1 Tawarmalani, Mohit 1 Toh, Kim Chuan 1 Ulbrich, Stefan 1 Wahba, Grace 1 Willcox, Karen E. 1 Wright, Stephen J. 1 Yamashita, Makoto 1 Ye, Yinyu all top 5 Cited in 18 Serials 3 Mathematical Programming. Series A. Series B 2 International Journal of Control 2 ACM Transactions on Mathematical Software 2 SIAM Journal on Optimization 2 Computational Optimization and Applications 2 Optimization Methods & Software 2 Mathematical Programming Computation 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Optimization Theory and Applications 1 Journal of Statistical Planning and Inference 1 Mathematics and Computers in Simulation 1 Networks 1 SIAM Journal on Matrix Analysis and Applications 1 Journal of Mathematical Imaging and Vision 1 International Transactions in Operational Research 1 INFORMS Journal on Computing 1 The Annals of Applied Statistics 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Cited in 12 Fields 27 Operations research, mathematical programming (90-XX) 9 Numerical analysis (65-XX) 6 Computer science (68-XX) 3 Statistics (62-XX) 3 Systems theory; control (93-XX) 2 Combinatorics (05-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year