# Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

Jingyong Tang; Li Dong; Liang Fang; Li Sun

Applications of Mathematics (2015)

- Volume: 60, Issue: 1, page 35-49
- ISSN: 0862-7940

## Access Full Article

top## Abstract

top## How to cite

topTang, Jingyong, et al. "Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming." Applications of Mathematics 60.1 (2015): 35-49. <http://eudml.org/doc/262175>.

@article{Tang2015,

abstract = {The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate that the non-monotone smoothing-type algorithm is promising for solving the SOCP.},

author = {Tang, Jingyong, Dong, Li, Fang, Liang, Sun, Li},

journal = {Applications of Mathematics},

keywords = {second-order cone programming; smoothing Newton algorithm; non-monotone line search; convergence; second-order cone programming; smoothing Newton algorithm; non-monotone line search; global convergence; local quadratic convergence},

language = {eng},

number = {1},

pages = {35-49},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming},

url = {http://eudml.org/doc/262175},

volume = {60},

year = {2015},

}

TY - JOUR

AU - Tang, Jingyong

AU - Dong, Li

AU - Fang, Liang

AU - Sun, Li

TI - Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming

JO - Applications of Mathematics

PY - 2015

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 60

IS - 1

SP - 35

EP - 49

AB - The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate that the non-monotone smoothing-type algorithm is promising for solving the SOCP.

LA - eng

KW - second-order cone programming; smoothing Newton algorithm; non-monotone line search; convergence; second-order cone programming; smoothing Newton algorithm; non-monotone line search; global convergence; local quadratic convergence

UR - http://eudml.org/doc/262175

ER -

## References

top- Alizadeh, F., Goldfarb, D., 10.1007/s10107-002-0339-5, Math. Program. 95 (2003), 3-51. (2003) Zbl1153.90522MR1971381DOI10.1007/s10107-002-0339-5
- Chi, X., Liu, S., 10.1080/02331930701763421, Optimization 58 (2009), 965-979. (2009) Zbl1177.90318MR2572781DOI10.1080/02331930701763421
- Chi, X., Liu, S., 10.1016/j.cam.2007.12.023, J. Comput. Appl. Math. 223 (2009), 114-123. (2009) Zbl1155.65045MR2463105DOI10.1016/j.cam.2007.12.023
- Clarke, F. H., Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts. John Wiley & Sons New York (1983); reprinted by SIAM, Philadelphia, 1990. Zbl0696.49002MR1058436
- Fang, L., Feng, Z., 10.1590/S1807-03022011000300005, Comput. Appl. Math. 30 (2011), 569-588. (2011) MR2863924DOI10.1590/S1807-03022011000300005
- Fang, L., He, G., Hu, Y., 10.1016/j.amc.2009.06.029, Appl. Math. Comput. 215 (2009), 1020-1029. (2009) Zbl1183.65065MR2568957DOI10.1016/j.amc.2009.06.029
- Fukushima, M., Luo, Z.-Q., Tseng, P., 10.1137/S1052623400380365, SIAM J. Optim. 12 (2002), 436-460. (2002) MR1885570DOI10.1137/S1052623400380365
- Grippo, L., Lampariello, F., Lucidi, S., 10.1137/0723046, SIAM J. Numer. Anal. 23 (1986), 707-716. (1986) Zbl0616.65067MR0849278DOI10.1137/0723046
- Hu, S.-L., Huang, Z.-H., Wang, P., 10.1080/10556780902769862, Optim. Methods Softw. 24 (2009), 447-460. (2009) Zbl1173.90552MR2533101DOI10.1080/10556780902769862
- Huang, Z. H., Han, J., Chen, Z., 10.1023/A:1023648305969, J. Optimization Theory Appl. 117 (2003), 39-68. (2003) Zbl1044.90081MR1990070DOI10.1023/A:1023648305969
- Huang, Z. H., Hu, S. L., Han, J., 10.1007/s11425-008-0170-4, Sci. China, Ser. A 52 (2009), 833-848. (2009) Zbl1203.90123MR2504979DOI10.1007/s11425-008-0170-4
- Huang, Z.-H., Ni, T., 10.1007/s10589-008-9180-y, Comput. Optim. Appl. 45 (2010), 557-579. (2010) Zbl1198.90373MR2600896DOI10.1007/s10589-008-9180-y
- Liu, X.-H., Huang, Z.-H., 10.1007/s00186-008-0274-1, Math. Methods Oper. Res. 70 (2009), 385-404. (2009) Zbl1175.90290MR2558418DOI10.1007/s00186-008-0274-1
- Liu, Y.-J., Zhang, L.-W., Wang, Y.-H., 10.1007/BF02896466, J. Appl. Math. Comput. 22 (2006), 133-148. (2006) Zbl1132.90353MR2248446DOI10.1007/BF02896466
- Lobo, M. S., Vandenberghe, L., Boyd, S., Lebret, H., Applications of second-order cone programming, Linear Algebra Appl. 284 (1998), 193-228. (1998) Zbl0946.90050MR1655138
- Ni, T., Wang, P., 10.1016/j.amc.2010.03.058, Appl. Math. Comput. 216 (2010), 2207-2214. (2010) Zbl1194.65080MR2647089DOI10.1016/j.amc.2010.03.058
- Pan, S., Chen, J.-S., 10.1007/s00245-008-9054-9, Appl. Math. Optim. 59 (2009), 293-318. (2009) Zbl1169.49031MR2491700DOI10.1007/s00245-008-9054-9
- Tang, J., He, G., Dong, L., Fang, L., 10.1016/j.amc.2011.06.015, Appl. Math. Comput. 218 (2011), 1317-1329. (2011) Zbl1229.65101MR2831640DOI10.1016/j.amc.2011.06.015
- Tang, J., He, G., Dong, L., Fang, L., 10.1007/s10492-012-0019-6, Appl. Math., Praha 57 (2012), 311-331. (2012) Zbl1265.90229MR2984606DOI10.1007/s10492-012-0019-6
- Zhang, H., Hager, W. W., 10.1137/S1052623403428208, SIAM J. Optim. 14 (2004), 1043-1056. (2004) Zbl1073.90024MR2112963DOI10.1137/S1052623403428208

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.