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Trust-region interior-point method for large sparse \(l_{1}\) optimization. (English) Zbl 1193.90197
Summary: We propose an interior-point method for large sparse \(l_{1}\) optimization. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus, relatively difficult \(l_{1}\) optimization problems can be solved successfully. The results of computational experiments given in this article confirm efficiency and robustness of the proposed method.

MSC:
90C30 Nonlinear programming
90C51 Interior-point methods
90C06 Large-scale problems in mathematical programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
Software:
GQTPAR; SNOPT; ve08
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[1] DOI: 10.1007/BF01582292 · Zbl 0724.90062 · doi:10.1007/BF01582292
[2] DOI: 10.1137/S0036144504446096 · Zbl 1210.90176 · doi:10.1137/S0036144504446096
[3] DOI: 10.1002/nla.354 · Zbl 1164.90422 · doi:10.1002/nla.354
[4] DOI: 10.1023/A:1008677427361 · Zbl 1040.90564 · doi:10.1023/A:1008677427361
[5] Lukšan L., Conjugate Gradient Algorithms and Finite Element Methods (2004)
[6] Fletcher R., Practical Methods of Optimization, 2. ed. (1987) · Zbl 0905.65002
[7] Powell M. J.D., Approximation Theory IV (1983)
[8] DOI: 10.1007/BF02591949 · Zbl 0577.90066 · doi:10.1007/BF02591949
[9] DOI: 10.1007/BF02612334 · Zbl 0572.65029 · doi:10.1007/BF02612334
[10] DOI: 10.1137/0904038 · Zbl 0551.65042 · doi:10.1137/0904038
[11] Powell M. J.D., Nonlinear Programming (1970)
[12] DOI: 10.1137/S105262349928887X · Zbl 0994.65067 · doi:10.1137/S105262349928887X
[13] DOI: 10.1137/0720042 · Zbl 0518.65042 · doi:10.1137/0720042
[14] Toint P. L., Sparse Matrices and Their Uses pp 57– (1981)
[15] DOI: 10.1007/BF01585529 · Zbl 0297.90082 · doi:10.1007/BF01585529
[16] DOI: 10.1093/imamat/23.2.235 · Zbl 0402.65018 · doi:10.1093/imamat/23.2.235
[17] DOI: 10.1007/BF02591998 · Zbl 0569.90069 · doi:10.1007/BF02591998
[18] DOI: 10.1137/1.9780898719857 · Zbl 0958.65071 · doi:10.1137/1.9780898719857
[19] Lukšan L., Pacific Journal on Optimization 2 pp 59–
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