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A filter active-set algorithm for ball/sphere constrained optimization problem. (English) Zbl 1342.65146
MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
Software:
ipfilter; Ipopt; L-BFGS; SNOPT
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References:
[1] C. Alexander, Common correlation and calibrating the lognormal forward rate model, Wilmott Mag., 2 (2003), pp. 68–78.
[2] L. Anderson, J. Sidenius, and S. Basu, All Your Hedges in One Basket, Risk. net, 2003, pp. 67–72.
[3] S. Bai, H.-D Qi, and N. Xiu, Constrained best Euclidean distance embedding on a sphere: A matrix optimization approach, SIAM J. on Optim., 25 (2015), pp. 439–467. · Zbl 1326.49043
[4] R. Borsdorf, N. J. Higham, and M. Raydan, Computing a nearest correlation matrix with factor structure, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2603–2622. · Zbl 1213.65022
[5] J. V. Burke, F. E. Curtis, and H. Wang, A sequential quadratic optimization algorithm with rapid infeasibility detection, SIAM J. Optim., 24 (2014), pp. 839–872. · Zbl 1301.49069
[6] R. M. Chamberlain, M. J. D. Powell, C. Lemarechal, and H. C. Pedersen, The watchdog technique for forcing convergence in algorithms for constrained optimization, Math. Program. Stud., 16 (1982), pp. 1–17. · Zbl 0477.90072
[7] L. F. Chen, Y. L. Wang, and G. P. He, A feasible active set QP-free method for nonlinear programming, SIAM J. Optim., 17 (2006), pp. 401–429. · Zbl 1165.90640
[8] N. Chiang and V. M. Zavala, An Inertia-Free Filter Line-Search Algorithm for Large-Scale Nonlinear Programming, http://www.optimization-online.org/DB_HTML/2014/09/4550.html (2014). · Zbl 1350.90031
[9] M. T. Chu and J. L. Watterson, On a multivariate eigenvalue problem: I. Algebraic theory and power method, SIAM J. Sci. Comput., 14 (1993), pp. 1089–1106. · Zbl 0789.65023
[10] A. R. Conn, N. I. M. Gould, and Ph. L. Toint, Trust-Region Methods, SIAM, Philadelphia, 2000.
[11] M. Crouhy, D. Galai, and R. Mark, A comparative analysis of current credit risk models, J. Banking Finance, 24 (2000), pp. 59–117.
[12] P. Glasserman and S. Suchintabandid, Correlation expansions for CDO pricing, J. Banking Finance, 31 (2007), pp. 1375–1398.
[13] F. Facchinei, A. Fischer, and C. Kanzow, On the accurate identification of active constraints, SIAM J. Optim., 9 (1998), pp. 14–32. · Zbl 0960.90080
[14] R. Fletcher, N. Gould, S. Leyffer, Ph.L. Toint, and A. Wächter, Global convergence of a trust-region SQP-filter allgorithm for general nonlinear programming, SIAM J. Optim., 13 (2002), pp. 635–659. · Zbl 1038.90076
[15] R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function, Math. Program, 91 (2002), pp. 239–269. · Zbl 1049.90088
[16] R. Fletcher, S. Leyffer, and Ph. L. Toint, On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13 (2002), pp. 44–59. · Zbl 1029.65063
[17] Z. Y. Gao, G. P. He, and F. Wu, An algorithm of sequential systems of linear equations for nonlinear optimization problems with arbitrary initial point, Sci. China Ser. A, 401 (1997), pp. 561–57. · Zbl 0886.90132
[18] P. E. Gill, W. Murray, and M. A. Saunders, SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM J. Optim., 12 (2002), pp. 979–1006. · Zbl 1027.90111
[19] N. Gould and D. P. Robinson, A second derivative SQP method: Global convergence, SIAM J. Optim., 20 (2010), pp. 2023–2048. · Zbl 1202.49039
[20] N. Gould and D. P. Robinson, A second derivative SQP method: Local convergence and practical issues, SIAM J. Optim., 20 (2010), pp. 2049–2079. · Zbl 1202.49040
[21] W. W. Hager and M. S. Gowda, Stability in the presence of degeneracy and error estimation, Math. Program, 85 (1999), pp. 181–192. · Zbl 0956.90049
[22] J. B. Jian and W. X. Cheng, A superlinearly convergent strongly sub-feasible SSLE-type algorithm with working set for nonlinearly constrained optimization, J. Comput. Appl. Math., 225 (2009), pp. 172–186. · Zbl 1162.65032
[23] B. Jiang and Y. H. Dai, A framework of constraint preserving update schemes for optimization on Stiefel manifold, Math. Program, 153 (2015), pp. 535–575. · Zbl 1325.49037
[24] E. Karas, A. Ribeiro, C. Sagastizbal, and M. Solodov, A bundle-filter method for nonsmooth convex constrained optimization, Math. Program., 116 (2009), pp. 297–320. · Zbl 1165.90024
[25] Q. N. Li, H. D. Qi, and N. H. Xiu, Block relaxation and majorization methods for the nearest correlation matrix with factor structure, Comput. Optim. Appl., 50 (2011), pp. 327–349. · Zbl 1236.90119
[26] D. C. Liu and J. Nocedal, On the limited memory method for large scale optimization, Math. Program. B, 45 (1989), pp. 503–528. · Zbl 0696.90048
[27] X. W. Liu and Y. X. Yuan, A sequential quadratic programming method without a penalty function or a filter for nonlinear equality constrained optimization, SIAM J. Optim., 21 (2011), pp. 545–571. · Zbl 1233.90257
[28] F. Lillo and R. N. Mantegna, Spectral density of the correlation matrix of factor models: A random matrix theory approach, Phys. Rev. E, 72 (2005), 016219.
[29] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer, New york, 2006. · Zbl 1104.65059
[30] C. Oberlin and S. J. Wright, Active set identification in nonlinear programming, SIAM J. Optim., 17 (2006), pp. 577–605. · Zbl 1174.90813
[31] E. R. Panier, A. L. Tits, and J. N. Herskovits, A QP-free globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization, SIAM J. Control Optim., 26 (1988), pp. 788–811. · Zbl 0651.90072
[32] H. D. Qi and L. Qi, A new QP-free globally convergent, locally superlinear convergent algorithm for inequality constrained optimization, SIAM J. Optim., 11 (2000), pp. 113–132. · Zbl 0999.90038
[33] H. D. Qi and D. F. Sun, A quadratically convergent Newton method for computing the nearest correlation matrix, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 360–385. · Zbl 1120.65049
[34] A. A. Ribeiro, E. W. Karas, and C. C. Gonzaga, Global convergence of filter methods for nonlinear programming, SIAM J. Optim., 19 (2008), pp. 1231–1249. · Zbl 1169.49034
[35] C. G. Shen, S. Leyffer, and R. Fletcher, A nonmonotone filter method for nonlinear optimization, Comput. Optim. Appl., 52 (2012), pp. 583–607. · Zbl 1259.90140
[36] C. G. Shen, W. J. Xue, and D.G. Pu, An infeasible SSLE filter algorithm for general constrained optimization without strict complementarity, Asia-Pac. J. Oper. Res., 28 (2011), pp. 361–399. · Zbl 1230.90183
[37] C. G. Shen, L. H. Zhang, B. Wang, and W. Q. Shao, Global and local convergence of a nonmonotone SQP Method for constrained nonlinear optimization, Comput. Optim. Appl., 59 (2014), pp. 435–473. · Zbl 1310.90107
[38] W. Y. Sun and Y. X. Yuan, Optimization Theory and Methods, in Nonlinear Programming, Springer, New York, 2006. · Zbl 1129.90002
[39] M. Ulbrich, S. Ulbrich, and L. N. Vicente, A globally convergent primal-dual interior-point filter method for nonlinear programming, Math. Program., 100 (2004), pp. 379–410. · Zbl 1070.90110
[40] A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Motivation and global convergence, SIAM J. Optim., 16 (2005), pp. 1–31. · Zbl 1114.90128
[41] A. Wächter and L. T. Biegler, Line search filter methods for nonlinear programming: Local convergence, SIAM J. Optim., 16 (2005), pp. 32–48. · Zbl 1115.90056
[42] A. Wächter and L. T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program., 106 (2006), pp. 25–57. · Zbl 1134.90542
[43] Y. L. Wang, L. F. Chen, and G. P. He, Sequential systems of linear equations method for general constrained optimization without strict complementarity, J. Comput. Appl. Math., 182 (2005), pp. 447–471. · Zbl 1078.65055
[44] Y. F. Yang, D. H. Li, and L. Q. Qi, A feasible sequential linear equation method for inequality constrained optimization, SIAM J. Optim., 13 (2003), pp. 1222–1244. · Zbl 1101.90394
[45] L. H. Zhang and M. T. Chu, Computing absolute maximum correlation, IMA J. Numer. Anal., 32 (2011), pp. 163–184. · Zbl 1239.65009
[46] L. H. Zhang, Riemannian trust-region method for the maximal correlation problem, Numer. Funct. Anal. Optim., 33 (2012), pp. 338–362. · Zbl 1296.62126
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