Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
unconstrained optimization; large-scale optimization; nonsmooth optimization; generalized minimax optimization; interior-point methods; modified Newton methods; variable metric methods; global convergence; computational experiments
unconstrained optimization; large-scale optimization; nonsmooth optimization; generalized minimax optimization; interior-point methods; modified Newton methods; variable metric methods; global convergence; computational experiments
Summary:
References:
[1] Bertsekas, D. P.: Nondifferentiable optimization via approximation. In: Nondifferentiable Optimization (M. L. Balinski and P.Wolfe, eds.), Math. Programming Stud. 3 (1975), 1–25. MR 0440906 | Zbl 0383.49025
[2] Coleman, T. F., Garbow, B. S., Moré, J. J.: Software for estimating sparse Hessian matrices. ACM Trans. Math. Software 11 (1985), 363–377. MR 0828562
[3] Coleman, T. F., Moré, J. J.: Estimation of sparse Hessian matrices and graph coloring problems. Math. Programming 28 (1984), 243–270. MR 0736293
[4] Demyanov, V. F., Malozemov, V. N.: Introduction to Minimax. Dover Publications, 1990. MR 1088479
[5] Fletcher, R.: Practical Methods of Optimization. Second edition. Wiley, New York 1987. MR 0955799 | Zbl 0905.65002
[6] Gill, P. E., Murray, W.: Newton type methods for unconstrained and linearly constrained optimization. Math. Programming 7 (1974), 311–350. MR 0356503 | Zbl 0297.90082
[7] Griewank, A.: Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia 2000. MR 1753583 | Zbl 0958.65028
[8] Griewank, A., Toint, P. L.: Partitioned variable metric updates for large-scale structured optimization problems. Numer. Math. 39 (1982), 119–137. MR 0664541
[9] Le, D.: Three new rapidly convergent algorithms for finding a zero of a function. SIAM J. Sci. Stat. Computat. 6 (1985), 193–208. MR 0773291 | Zbl 0561.65033
[10] Le, D.: An efficient derivative-free method for solving nonlinear equations. ACM Trans. Math. Software 11 (1985), 250–262. MR 0814340 | Zbl 0581.65033
[11] Lukšan, L., Matonoha, C., Vlček, J.: Interior point method for nonlinear nonconvex optimization. Numer. Linear Algebra Appl. 11 (2004), 431–453. MR 2067814
[12] Lukšan, L., Matonoha, C., Vlček, J.: On Lagrange multipliers of trust-region subproblems. BIT Numer. Math. 48 (2008), 763–768. MR 2465702 | Zbl 1203.65092
[13] Lukšan, L., Matonoha, C., Vlček, J.: Primal interior-point method for large sparse minimax optimization. Kybernetika 45 (2009), 841–864. MR 2599116 | Zbl 1198.90394
[14] Lukšan, L., Matonoha, C., Vlček, J.: Trust-region interior-point method for large sparse $l_1$ optimization. Optimization Methods and Software 22 (2007), 737–753. MR 2354765 | Zbl 1193.90197
[15] Lukšan, L., Spedicato, E.: Variable metric methods for unconstrained optimization and nonlinear least squares. J. Comput. Appl. Math. 124 (2000), 61–93. MR 1803294
[16] Lukšan, L., Vlček, J.: Sparse and Partially Separable Test Problems for Unconstrained and Equality Constrained Optimization. Technical Report V-767, ICS AS ČR, Prague 1998.
[17] Lukšan, L., Vlček, J.: Variable metric method for minimization of partially separable nonsmooth functions. Pacific J. Optim. 2 (2006), 59–70. MR 2548209
[18] Pillo, G. Di, Grippo, L., Lucidi, S.: Smooth transformation of the generalized minimax problem. J. Optim. Theory Appl. 95 (1997), 1–24. MR 1477348 | Zbl 0890.90165
[19] Vanderbei, J., Shanno, D. F.: An interior point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl. 13 (1999), 231–252. MR 1704122 | Zbl 1040.90564
[20] Xu, S.: Smoothing methods for minimax problems. Computational Optim. Appl. 20 (2001), 267–279. MR 1857058
Search
Partner of
