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An interior-point trust-funnel algorithm for nonlinear optimization. (English) Zbl 1355.65075
The authors present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The given algorithm achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, but has the additional capability of being able to solve problems with both equality and inequality constraints. A flow diagram of the given trust-funnel algorithm is presented.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
90C26 Nonconvex programming, global optimization
Full Text: DOI
[1] Argáez, M; Tapia, R, On the global convergence of a modified augmented Lagrangian linesearch interior-point Newton method for nonlinear programming, J Optim Theory Appl, 114, 1-25, (2002) · Zbl 1009.90111
[2] Byrd, RH; Curtis, FE; Nocedal, J, An inexact SQP method for equality constrained optimization, SIAM J. Optim., 19, 351-369, (2008) · Zbl 1158.49035
[3] Byrd, RH; Gilbert, JC; Nocedal, J, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89, 149-185, (2000) · Zbl 1033.90152
[4] Byrd, RH; Hribar, ME; Nocedal, J, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9, 877-900, (1999) · Zbl 0957.65057
[5] Conn, A.R., Gould, N.I.M., Toint, Ph.L.: Trust-Region Methods. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000) · Zbl 0958.65071
[6] Curtis, FE; Schenk, O; Wächter, A, An interior-point algorithm for large-scale nonlinear optimization with inexact step computations, SIAM J. Sci. Comput., 32, 3447-3475, (2010) · Zbl 1220.49018
[7] Czyzyk, J; Fourer, R; Mehrotra, S, Using a massively parallel processor to solve large sparse linear programs by an interior-point method, SIAM J. Sci. Comput., 19, 553-565, (1998) · Zbl 0913.65048
[8] Fletcher, R.: Practical Methods of Optimization. Wiley-Interscience (Wiley), New York (2001) · Zbl 0988.65043
[9] Fletcher, R., Gould, N.I.M., Leyffer, S., Toint, Ph.L., Wächter, A.: Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming. SIAM J. Optim. 13, 635-659 (2002). [(electronic) (2003)] · Zbl 1038.90076
[10] Fletcher, R; Leyffer, S, Nonlinear programming without a penalty function, Math. Program., 91, 239-269, (2002) · Zbl 1049.90088
[11] Fletcher, R., Leyffer, S., Toint, Ph.L.: On the global convergence of a filter-SQP algorithm. SIAM J. Optim. 13, 44-59 (2002) · Zbl 1029.65063
[12] Fourer, R; Mehrotra, S, Performance of an augmented system approach for solving least-squares problems in an interior-point method for linear programming, Math. Program., 19, 26-31, (1991)
[13] Fourer, R; Mehrotra, S, Solving symmetric indefinite systems in an interior-point method for linear programming, Math. Program., 62, 15-39, (1993) · Zbl 0802.90069
[14] Gertz, EM; Gill, PE, A primal-dual trust region algorithm for nonlinear optimization, Math. Program Ser. B, 100, 49-94, (2004) · Zbl 1146.90514
[15] Gill, PE; Murray, W; Saunders, MA, SNOPT: an SQP algorithm for large-scale constrained optimization, SIAM Rev., 47, 99-131, (2005) · Zbl 1210.90176
[16] Gill, P.E., Murray, W., Wright, M.H.: Practical Optimization. Academic Press Inc. (Harcourt Brace Jovanovich Publishers), London (1981) · Zbl 0503.90062
[17] Gondzio, J, Interior point methods 25 years later, Eur. J. Oper. Res., 218, 587-601, (2012) · Zbl 1244.90007
[18] Gould, N.I.M., Orban, D., Toint, Ph.L.: GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Softw. 29, 353-372 (2003) · Zbl 1068.90525
[19] Gould, NIM; Robinson, DP, A second derivative SQP method: global convergence, SIAM J. Optim., 20, 2023-2048, (2010) · Zbl 1202.49039
[20] Gould, NIM; Robinson, DP, A second derivative SQP method: local convergence and practical issues, SIAM J. Optim., 20, 2049-2079, (2010) · Zbl 1202.49040
[21] Gould, NIM; Robinson, DP, A second derivative SQP method with a “trust-region-free” predictor step, IMA J. Numer. Anal., 32, 580-601, (2012) · Zbl 1246.65089
[22] Gould, N.I.M., Robinson, D.P., Thorne, H.S.: On solving trust-region and other regularised subproblems in optimization. Math. Program. Comput. 2, 21-57 (2010) · Zbl 1193.65098
[23] Gould, N.I.M., Toint, Ph.L.: Nonlinear programming without a penalty function or a filter. Math. Program. 122, 155-196 (2010) · Zbl 1216.90069
[24] Karmarkar, N, A new polynomial-time algorithm for linear programming, Combinatorica, 4, 373-395, (1984) · Zbl 0557.90065
[25] Karush, W.: Minima of Functions of Several Variables with Inequalities as Side Conditions. Master’s thesis, Department of Mathematics, University of Chicago, Illinois, USA (1939)
[26] Kuhn, HW; Tucker, AW; Neyman, J (ed.), Nonlinear programming, (1951), California
[27] Lalee, M; Nocedal, J; Plantenga, T, On the implementation of an algorithm for large-scale equality constrained optimization, SIAM J. Optim., 8, 682-706, (1998) · Zbl 0913.65055
[28] Mehrotra, S, On the implementation of a primal-dual interior point method, SIAM J. Optim., 2, 575-601, (1992) · Zbl 0773.90047
[29] Morales, JL; Nocedal, J; Wu, Y, A sequential quadratic programming algorithm with an additional equality constrained phase, IMA J. Numer. Anal., 32, 553-579, (2012) · Zbl 1246.65093
[30] Orban, D; Gould, NIM; Robinson, DP, Trajectory-following methods for large-scale degenerate convex quadratic programming, Math. Program. Comput., 5, 113-142, (2013) · Zbl 1272.65051
[31] Vanderbei, RJ, LOQO: an interior point code for quadratic programming, Optim. Methods Softw., 11, 451-484, (1999) · Zbl 0973.90518
[32] Wächter, A; Biegler, LT, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming, Math. Program. Ser. A, 106, 25-57, (2006) · Zbl 1134.90542
[33] Yabe, H; Yamashita, H, Q-superlinear convergence of primal-dual interior point quasi-Newton methods for constrained optimization, J. Oper. Res. Soc. Jpn., 40, 415-436, (1997) · Zbl 0914.90246
[34] Yamashita, H; Yabe, H, Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization, Math. Program., 75, 377-397, (1996) · Zbl 0874.90175
[35] Yamashita, H; Yabe, H, An interior point method with a primal-dual quadratic barrier penalty function for nonlinear optimization, SIAM J. Optim., 14, 479-499, (2003) · Zbl 1072.90050
[36] Yamashita, H; Yabe, H; Tanabe, T, A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization, Math. Program. Ser. A, 102, 111-151, (2005) · Zbl 1062.90036
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