References
References¶
- 1
F. Alizadeh and D. Goldfarb. Second-order cone programming. Mathematical Programming, 95(1):3–51, 2003. doi:10.1007/s10107-002-0339-5.
- 2
E. D. Andersen. Handling free variables in primal-dual interior-point methods using a quadratic cone. 2002. URL: https://meetings.siam.org/sess/dsp_talk.cfm?p=3815.
- 3
M. Anjos and S. Burer. On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization. SIAM Journal on Optimization, 18(4):1310–1325, 2007. doi:10.1137/06066847X.
- 4
B. Borchers. CSDP 6.2.0 User's Guide. 2017. URL: https://github.com/coin-or/Csdp/blob/master/doc/csdpuser.pdf.
- 5
Brian Borchers. CSDP 2.3 user's guide. Optimization Methods and Software, 11(1-4):597–611, 1999. doi:10.1080/10556789908805764.
- 6
D. Chaykin, C. Jansson, F. Keil, M. Lange, K. T. Ohlhus, and S. M. Rump. Rigorous results in electronic structure calculations. 2016. URL: http://www.optimization-online.org/DB_HTML/2016/11/5730.html.
- 7
L. El Ghaoui and H. Lebret. Robust Solutions to Least-Squares Problems with Uncertain Data. SIAM Journal on Matrix Analysis and Applications, 18(4):1035–1064, 1997. doi:10.1137/S0895479896298130.
- 8
Robert M. Freund, Fernando Ordóñez, and Kim-Chuan Toh. Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems. Mathematical Programming, 109(2):445–475, 2007. doi:10.1007/s10107-006-0035-y.
- 9
V. Härter, C. Jansson, and M. Lange. VSDP: A Matlab toolbox for verified semidefinite-quadratic-linear programming. 2012. URL: http://www.optimization-online.org/DB_HTML/2013/01/3724.html.
- 10
C. Jansson. VSDP: Verified SemiDefinite Programming. 2006. URL: http://www.optimization-online.org/DB_HTML/2006/12/1547.html.
- 11
C. Jansson, D. Chaykin, and C. Keil. Rigorous Error Bounds for the Optimal Value in Semidefinite Programming. SIAM Journal on Numerical Analysis, 46(1):180–200, 2007. doi:10.1137/050622870.
- 12
Christian Jansson. A Rigorous Lower Bound for the Optimal Value of Convex Optimization Problems. Journal of Global Optimization, 28(1):121–137, 2004. doi:10.1023/B:JOGO.0000006720.68398.8c.
- 13
Christian Jansson. Guaranteed Accuracy for Conic Programming Problems in Vector Lattices. arXiv:0707.4366 [math], 2007. arXiv:0707.4366.
- 14
Christian Jansson. On verified numerical computations in convex programming. Japan Journal of Industrial and Applied Mathematics, 26(2):337–363, 2009. doi:10.1007/BF03186539.
- 15
Kazuhiro Kobayashi, Kazuhide Nakata, and Masakazu Kojima. A conversion of an SDP having free variables into the standard form SDP. Computational Optimization and Applications, 36(2):289–307, 2007. doi:10.1007/s10589-006-9002-z.
- 16
M. Kočvara. On the modelling and solving of the truss design problem with global stability constraints. Structural and Multidisciplinary Optimization, 23(3):189–203, 2002. doi:10.1007/s00158-002-0177-3.
- 17
Csaba Mészáros. On free variables in interior point methods. Optimization Methods and Software, 9(1-3):121–139, 1998. doi:10.1080/10556789808805689.
- 18
Maho Nakata, Bastiaan J. Braams, Katsuki Fujisawa, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, and Zhengji Zhao. Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver. The Journal of Chemical Physics, 128(16):164113, 2008. doi:10.1063/1.2911696.
- 19
F. Ordóñez and R. Freund. Computational Experience and the Explanatory Value of Condition Measures for Linear Optimization. SIAM Journal on Optimization, 14(2):307–333, 2003. doi:10.1137/S1052623402401804.
- 20
G. Pataki and S. H. Schmieta. The DIMACS library of mixed semidefinite-quadratic-linear programs. Techreport, Columbia University, 2002. URL: http://dimacs.rutgers.edu/archive/Challenges/Seventh/.
- 21
James Renegar. Some perturbation theory for linear programming. Mathematical Programming, 65(1):73–91, 1994. doi:10.1007/BF01581690.
- 22
Siegfried M. Rump. INTLAB — INTerval LABoratory. In Tibor Csendes, editor, Developments in Reliable Computing, pages 77–104. Springer Netherlands, 1999. doi:10.1007/978-94-017-1247-7_7.
- 23
Siegfried M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19:287–449, 2010. doi:10.1017/S096249291000005X.
- 24
L. Vandenberghe and S. Boyd. Semidefinite Programming. SIAM Review, 38(1):49–95, 1996. doi:10.1137/1038003.
- 25
Zhengji Zhao, Bastiaan J. Braams, Mituhiro Fukuda, Michael L. Overton, and Jerome K. Percus. The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions. The Journal of Chemical Physics, 120(5):2095–2104, 2004. doi:10.1063/1.1636721.
- 26
Jochem Zowe, Michal Kočvara, and Martin P. Bendsøe. Free material optimization via mathematical programming. Mathematical Programming, 79(1):445–466, 1997. doi:10.1007/BF02614328.
- 27
A. Ben-Tal, M. Kovara, A. Nemirovski, and J. Zowe. Free Material Design via Semidefinite Programming: The Multiload Case with Contact Conditions. SIAM Review, 42(4):695–715, 2000. doi:10.1137/S0036144500372081.
- 28
A. Ben-Tal and A. Nemirovski. Lectures on Modern Convex Optimization. MOS-SIAM Series on Optimization. Society for Industrial and Applied Mathematics, 2001. ISBN 978-0-89871-491-3. doi:10.1137/1.9780898718829.