Abstract
This work gives an overview of the major codes available for the solution of linear semidefinite (SDP) and second-order cone (SOCP) programs. Many of these codes also solve linear programs (LP). Some developments since the 7th DIMACS Challenge [10, 18] are pointed out as well as some currently under way. Instead of presenting performance tables, reference is made to the ongoing benchmark webpage [20] as well as other related efforts.
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References
Andersen, M.S., Dahl, J., Vandenberghe, L.: Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones. Mathematical Programming Computation 2(3–4), 167–201 (2010)
Andersen, E.D., Roos, C., Terlaky, T.: On implementing a primal-dual interior-point method for conic quadratic optimization. Mathematical Programming (series B) 95, 249–277 (2003)
Armbruster, M., Fügenschuh, M., Helmberg, C., Martin, A.: A Comparative Study of Linear and Semidefinite Branch-and-Cut Methods for Solving the Minimum Graph Bisection Problem. In: Lodi, A., Panconesi, A., Rinaldi, G. (eds.) Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, pp. 112–124. Springer (2008)
Benson, H.Y., Vanderbei, R.J.: Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming. Mathematical Programming Ser. B 95, 279–302 (2003)
Benson, S.J., Ye, Y.: Algorithm 875: DSDP5—software for semidefinite programming. ACM Trans. Math. Software 34(3), Art. 16 (2008)
Borchers, B.: CSDP, A C library for semidefinite programming. Optimization Methods and Software 11, 613–623 (1999)
Borchers, B., Young, J.: Implementation of a Primal-Dual Method for SDP on a Shared Memory Parallel Architecture. Comp. Opt. Appl. 37, 355–369 (2007)
Burer, S., Monteiro, R.D.C.: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization. Mathematical Programming (series B) 95, 329–357 (2003)
Burer, S., Monteiro, R.D.C.: Local minima and convergence in low-rank semidefinite programming. Mathematical Programming (series A) 103, 427–444 (2005)
DIMACS 7th Challenge website, http://dimacs.rutgers.edu/Challenges/Seventh/ (2000)
Fujisawa, K., Fukuda, M., Kobayashi, K., Kojima, M., Nakata, K., Nakata, M., Yamashita, M.: SDPA (SemiDefinite Programming Algorithm) User’s Manual — Version 7.0.5 Research Report B-448, Dept. of Math. and Comp. Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152-8552, January 2010.
Gijswijt, D.C., Mittelmann, H.D., Schrijver, A.: Semidefinite code bounds based on quadruple distances, IEEE Transaction on Information Theorem, to appear
Helmberg, C.: A Cutting Plane Algorithm for Large Scale Semidefinite Relaxations. In: Grötschel, M. (ed.) The Sharpest Cut, MPS-SIAM Series on Optimization, 233–256 (2004)
Helmberg, C., Rendl, F., Vanderbei, R.J., Wolkowicz, H.: An interior-point method for semidefinite programming, SIAM Journal on Optimization 6, 342–361 (1996)
Helmberg, C., Rendl, F.: A spectral bundle method for semidefinite programming. SIAM Journal on Optimization 10, 673–696 (2000)
Helmberg, C., Kiwiel, K.C.: A Spectral Bundle Method with Bounds. Mathematical Programming Ser. B 93, 173–194 (2002)
Kojima, M., Shindoh, S., Hara, S.: Interior-point methods for the monotone semidefinite linear complementarity problems. SIAM Journal on Optimization 7, 86–125 (1997)
Mittelmann, H.D.: An independent benchmarking of SDP and SOCP solvers. Mathematical Programming (series B) 95, 407–430 (2003)
Mittelmann, H.D.: Decision Tree for Optimization Software. http://plato.la.asu.edu/guide.html (2011)
Mittelmann, H.D.: Benchmarks for Optimization Software. http://plato.la.asu.edu/bench.html (2011)
Mittelmann, H. D., Vallentin, F.: High Accuracy Semidefinite Programming Bounds for Kissing Numbers. to appear in Experimental Mathematics (2010)
NEOS Server for Optimization. http://www-neos.mcs.anl.gov/neos/ (2011)
Polik, I.: Conic optimization software. In Encyclopedia of Operations Research, Wiley (2010)
Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11, 625–653 (1999)
Sturm, J.F.: Central region method, In: Frenk, J.B.G. Roos, C., Terlaky, T., Zhang, S. (eds.) High Performance Optimization, pp. 157–194. Kluwer Academic Publishers (2000)
Tütüncü, R.H., Toh, K.C., Todd, M.J.: Solving semidefinite-quadratic-linear programs using SDPT3. Mathematical Programming Ser. B 95, 189–217 (2003)
Yamashita, M., Fujisawa, K., Nakata, K., Nakata, M., Fukuda, M., Kobayashi, K., Goto, K.: A high-performance software package for semidefinite programs: SDPA 7. Research Report B-460, Dept. of Math. and Comp. Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152-8552, January 2010.
Ye, Y., Todd, M.J., Mizuno, S.: An \(O(\sqrt{n}L)\)-iteration homogeneous and self–dual linear programming algorithm. Mathematics of Operations Research 19, 53–67 (1994)
Zhao, X.-Y., Sun, D., Toh, K.-C.: A Newton-CG Augmented Lagrangian Method for Semidefinite Programming. SIAM Journal on Optimization 20, 1737–1765 (2010)
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Mittelmann, H.D. (2012). The State-of-the-Art in Conic Optimization Software. In: Anjos, M.F., Lasserre, J.B. (eds) Handbook on Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science, vol 166. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0769-0_23
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