SCS swMATH ID: 16632 Software Authors: B. O'Donoghue, E. Chu, N. Parikh, S. Boyd Description: SCS: Splitting conic solver: Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding. We introduce a first order method for solving very large cone programs to modest accuracy. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent feasibility problem involving finding a nonzero point in the intersection of a subspace and a cone. This approach has several favorable properties. Compared to interior-point methods, first-order methods scale to very large problems, at the cost of lower accuracy. Compared to other first-order methods for cone programs, our approach finds both primal and dual solutions when available and certificates of infeasibility or unboundedness otherwise, it does not rely on any explicit algorithm parameters, and the per-iteration cost of the method is the same as applying the splitting method to the primal or dual alone. We discuss efficient implementation of the method in detail, including direct and indirect methods for computing projection onto the subspace, scaling the original problem data, and stopping criteria. We describe an open-source implementation called SCS, which handles the usual (symmetric) nonnegative, second-order, and semidefinite cones as well as the (non-self-dual) exponential and power cones and their duals. We report numerical results that show speedups over interior-point cone solvers for large SOCPs, and scaling to very large general cone programs. Homepage: https://github.com/cvxgrp/scs Source Code: https://github.com/cvxgrp/scs Related Software: Mosek; CVXPY; GitHub; ECOS; Julia; SDPT3; YALMIP; JuMP; CVX; OSQP; SeDuMi; CPLEX; Gurobi; SuperMann; Benchmarks for Optimization Software; SDPLIB; CSparse; Ipopt; SDPNAL+; POGS Cited in: 64 Publications all top 5 Cited by 139 Authors 11 Boyd, Stephen Poythress 6 Goulart, Paul J. 4 Fantuzzi, Giovanni 3 Diamond, Steven 3 Kaluba, Marek 3 Lubin, Miles 3 Nowak, Piotr W. 3 O’Donoghue, Brendan 3 Vielma, Juan Pablo 2 Banjac, Goran 2 Coey, Chris 2 Elamvazhuthi, Karthik 2 Fu, Anqi 2 Garcia, Joaquim Dias 2 Grover, Piyush 2 Hütter, Jan-Christian 2 Mao, Cheng 2 Mazumder, Rahul 2 Müller, Christian L. 2 Necoara, Ion 2 Rapoport, Lev B. 2 Rigollet, Philippe 2 Robeva, Elina 2 Rontsis, Nikitas 2 Stellato, Bartolomeo 2 Wynn, Andrew 2 Zhang, Junzi 1 Açıkmeşe, Behçet 1 Allen, Larry 1 Allmaras, Steven R. 1 Andersen, Erling D. 1 Andersen, Martin S. 1 Ang, Andrew 1 Angeris, Guillermo 1 Askari, Armin 1 Barratt, Shane 1 Bemporad, Alberto 1 Bent, Russell W. 1 Bien, Jacob 1 Busseti, Enzo 1 Cannon, Mark 1 Carson, Hugh A. 1 Cevher, Volkan 1 Chen, Run 1 Chernyshenko, Sergei I. 1 Chklovskii, Dmitri B. 1 Combettes, Patrick L. 1 Dahl, Joachim 1 Darmofal, David L. 1 d’Aspremont, Alexandre 1 De Marchi, Alberto 1 Deford, Daryl R. 1 Ding, Lijun 1 Dowson, Oscar 1 East, Sebastian 1 Elango, Purnanand 1 Eltved, Anders 1 Friberg, Henrik A. 1 Galbraith, Marshall C. 1 Garstka, Michael 1 Gaynanova, Irina 1 Glaser, Lisa 1 Glineur, François 1 Gnacik, Michał 1 Goluskin, David 1 Grün, Bettina 1 Guzik, Marcin 1 Hornik, Kurt 1 Jin, Ming 1 Jin, Yimin 1 Josz, Cédric 1 Kania, Tomasz 1 Kapelevich, Lea 1 Khamaru, Koulik 1 Kielak, Dawid 1 Kirby, Robert C. 1 Kochenderfer, Mykel J. 1 Kroer, Christian 1 Lakshmi, Mayur V. 1 Lasagna, Davide 1 Lavaei, Javad 1 Lederer, Johannes 1 Legat, Benoît 1 Li, Yongfeng 1 Li, Zhizhi 1 Liberti, Leo 1 Lin, Tianyi 1 Liu, Andrew L. 1 Liu, Haoyang 1 Lu, Haihao 1 Ma, Shiqian 1 Madani, Ramtin 1 Milz, Johannes 1 Moehle, Nicholas 1 Moursi, Walaa M. 1 Nakatsukasa, Yuji 1 Nesterov, Yurii 1 Osborne, Michael A. 1 Ou-Yang, Le 1 Ozawa, Narutaka ...and 39 more Authors all top 5 Cited in 36 Serials 8 SIAM Journal on Optimization 6 Journal of Optimization Theory and Applications 3 Mathematical Programming. Series A. Series B 3 Computational Optimization and Applications 3 INFORMS Journal on Computing 3 Optimization and Engineering 3 Journal of Machine Learning Research (JMLR) 2 SIAM Journal on Scientific Computing 2 Optimization Methods & Software 2 Mathematical Programming Computation 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Journal of Geometry and Physics 1 Automatica 1 Mathematische Annalen 1 Numerische Mathematik 1 Operations Research 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Physica D 1 Optimization 1 Numerical Algorithms 1 Computational Statistics 1 Automation and Remote Control 1 European Journal of Operational Research 1 Top 1 Bernoulli 1 European Journal of Control 1 Annals of Mathematics. Second Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Electronic Journal of Statistics 1 Groups, Complexity, Cryptology 1 Journal of Computational and Graphical Statistics 1 Journal of Computational Dynamics 1 SIAM Journal on Mathematics of Data Science all top 5 Cited in 22 Fields 49 Operations research, mathematical programming (90-XX) 16 Numerical analysis (65-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Statistics (62-XX) 6 Computer science (68-XX) 3 Group theory and generalizations (20-XX) 3 Topological groups, Lie groups (22-XX) 3 Systems theory; control (93-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Mathematics education (97-XX) Citations by Year