×

zbMATH — the first resource for mathematics

Minimal conic quadratic reformulations and an optimization model. (English) Zbl 07165831
Summary: In this paper, we consider a particular form of inequalities which involves product of multiple variables with rational exponents. These inequalities can equivalently be represented by a number of conic quadratic forms called cone constraints. We propose an integer programming model and a heuristic algorithm to obtain the minimum number of cone constraints which equivalently represent the original inequality. The performance of the proposed algorithm and the computational effect of reformulations are numerically illustrated.
MSC:
90 Operations research, mathematical programming
Software:
ECOS; SDPT3; SeDuMi; YALMIP
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aktürk, M. S.; Atamtürk, A.; GüRel, S., A strong conic quadratic reformulation for machine-job assignment with controllable processing times, Oper. Res. Lett., 37, 3, 187-191 (2009) · Zbl 1167.90518
[2] Alizadeh, F.; Goldfarb, D., Second-order cone programming, Math. Program., 95, 1, 3-51 (2003) · Zbl 1153.90522
[3] Ben-Tal, A.; Nemirovski, A., Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, Vol. 2 (2001), Siam · Zbl 0986.90032
[4] Ben-Tal, A.; Nemirovski, A., On polyhedral approximations of the second-order cone, Math. Oper. Res., 26, 2, 193-205 (2001) · Zbl 1082.90133
[5] A. Domahidi, E. Chu, S. Boyd, ECOS: An SOCP solver for embedded systems, in: European Control Conference, ECC, 2013, pp. 3071-3076.
[6] Friberg, H. A., Power cones in second-order cone form and dual recovery (2017), https://docs.mosek.com/slides/2017/siopt/powcones.pdf (Accessed January 2019)
[7] Krokhmal, P. A., Higher moment coherent risk measures, Quant. Finance, 7, 4, 373-387 (2007) · Zbl 1190.91074
[8] Lobo, M. S.; Vandenberghe, L.; Boyd, S.; Lebret, H., Applications of second-order cone programming, Linear Algebra Appl., 284, 1-3, 193-228 (1998) · Zbl 0946.90050
[9] J. Löfberg, Yalmip: A toolbox for modeling and optimization in matlab, in: Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
[10] Morenko, Y.; Vinel, A.; Yu, Z.; Krokhmal, P., On p-norm linear discrimination, European J. Oper. Res., 231, 3, 784-789 (2013) · Zbl 1317.90230
[11] Sturm, J., Using SeDuMi 1.02, A MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw., 11-12, 625-653 (1999), Version 105 available from http://fewcal.kub.nl/sturm · Zbl 0973.90526
[12] Toh, K. C.; Todd, M.; Tütüncü, R. H., Sdpt3 - A matlab software package for semidefinite programming, Optim. Methods Softw., 11, 545-581 (1999) · Zbl 0997.90060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.