Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
sensitivity; quadratic second-order cone programming; nonlinear second-order cone programming; local convergence
sensitivity; quadratic second-order cone programming; nonlinear second-order cone programming; local convergence
Summary:
In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence analysis done before, we do not need the assumption that the Hessian matrix of the Lagrangian function is positive definite. Besides, the iteration sequence which is proved to be superlinearly convergent does not contain the Lagrangian multiplier.
References:
[1] Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program. 95 (2003), 3-51. DOI 10.1007/s10107-002-0339-5 | MR 1971381 | Zbl 1153.90522
[2] Bonnans, J. F., Ramírez, C. H.: Perturbation analysis of second-order cone programming problems. Math. Program. 104 (2005), 205-207. DOI 10.1007/s10107-005-0613-4 | MR 2179235 | Zbl 1124.90039
[3] Bonnans, J. F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer, New York (2000). DOI 10.1007/978-1-4612-1394-9 | MR 1756264 | Zbl 0966.49001
[4] Freund, R. W., Jarre, F., Vogelbusch, C. H.: Nonlinear semidefinite programming: Sensitivity,convergence, and an application in passive reduced-order modeling. Math. Program. 109 (2007), 581-611. DOI 10.1007/s10107-006-0028-x | MR 2296565 | Zbl 1147.90030
[5] Fukuda, E. H., Fukushima, M.: The use of squared slack variables in nonlinear second-order cone programming. J. Optim. Theory Appl. 170 (2016), 394-418. DOI 10.1007/s10957-016-0904-3 | MR 3527702 | Zbl 1346.90767
[6] Fukuda, E. H., Silva, P. J. S., Fukushima, M.: Differentiable exact penalty functions for nonlinear second-order cone programs. SIAM J. Optim. 22 (2012), 1607-1633. DOI 10.1137/110852401 | MR 3029794 | Zbl 1261.49006
[7] Garcés, R., Gómez, W., Jarre, F.: A sensitivity result for quadratic semidefinite programs with an application to a sequential quadratic semidefinite programming algorithm. Comput. Appl. Math. 31 (2012), 205-218. DOI 10.1590/S1807-03022012000100011 | MR 2924763 | Zbl 1254.90153
[8] Kanzow, C., Ferenczi, I., Fukushima, M.: On the local convergence of semismooth Newton methods for linear and nonlinear second-order cone programs without strict complementarity. SIAM J. Optim. 20 (2009), 297-320. DOI 10.1137/060657662 | MR 2496902 | Zbl 1190.90239
[9] Kato, H., Fukushima, M.: An SQP-type algorithm for nonlinear second-order cone programs. Optim. Lett. 1 (2007), 129-144. DOI 10.1007/s11590-006-0009-2 | MR 2357594 | Zbl 1149.90149
[10] Lobo, M. S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra Appl. 284 (1998), 193-228. DOI 10.1016/S0024-3795(98)10032-0 | MR 1655138 | Zbl 0946.90050
[11] Pang, J.-S., Sun, D., Sun, J.: Semismooth homeomorphisms and strong stability of semidefinite and Lorentz cone complementarity problems. Math. Oper. Res. 28 (2003), 39-63. DOI 10.1287/moor.28.1.39.14258 | MR 1961266 | Zbl 1082.90115
[12] Qi, L., Sun, J.: A nonsmooth version of Newton's method. Math. Program. 58 (1993), 353-367. DOI 10.1007/BF01581275 | MR 1216791 | Zbl 0780.90090
[13] Sun, D.: The strong second-order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications. Math. Oper. Res. 31 (2006), 761-776. DOI 10.1287/moor.1060.0195 | MR 2281228 | Zbl 1278.90304
[14] Wang, Y., Zhang, L.: Properties of equation reformulation of the Karush-Kuhn-Tucker condition for nonlinear second order cone optimization problems. Math. Meth. Oper. Res. 70 (2009), 195-218. DOI 10.1007/s00186-008-0241-x | MR 2558410 | Zbl 1190.49031
Search
Partner of
