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Copositivity meets D. C. optimization
1. | Aix-Marseille Université, Laboratoire d'Informatique et Systèmes, (LIS UMR 7020 CNRS/AMU/UTLN), Marseille, France |
2. | Université des Antilles, 97233 Martinique, F.W.I |
Based on a work by M. Dur and J.-B. Hiriart-Urruty[
References:
[1] |
F. J. Aragón Artacho, R. Campoy and P. T. Vuong, The Boosted DC Algorithm for linearly constrained DC programming, preprint, arXiv: 1908.01138. |
[2] |
P. L. Combettes and V. R. Wajs,
Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200.
doi: 10.1137/050626090. |
[3] |
M. Dür and J.-B. Hiriart-Urruty,
Testing copositivity with the help of difference-of-convex optimization, Math. Program., 140 (2013), 31-43.
doi: 10.1007/s10107-012-0625-9. |
[4] |
J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms. I. Fundamentals, Grundlehren der Mathematischen Wissenschaften, 305, Springer-Verlag, Berlin, 1993.
doi: 10.1007/978-3-662-02796-7. |
[5] |
J.-B. Hiriart-Urruty and A. Seeger,
A variational approach to copositive matrices, SIAM Rev., 52 (2010), 593-629.
doi: 10.1137/090750391. |
[6] |
A. Moudafi and P.-E. Maingé,
On the convergence of an approximate proximal method for DC functions, J. Comput. Math., 24 (2006), 475-480.
|
[7] |
J. C. O. Souza, P. R. Oliveira and A. Soubeyran,
Global convergence of a proximal linearized algorithm for difference of convex functions, Optim. Lett., 10 (2016), 1529-1539.
doi: 10.1007/s11590-015-0969-1. |
[8] |
W.-Y. Sun, R. J. B. Sampaio and M. A. B. Candido,
Proximal point algorithm for minimization of DC function, J. Comput. Math., 21 (2003), 451-462.
|
show all references
References:
[1] |
F. J. Aragón Artacho, R. Campoy and P. T. Vuong, The Boosted DC Algorithm for linearly constrained DC programming, preprint, arXiv: 1908.01138. |
[2] |
P. L. Combettes and V. R. Wajs,
Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200.
doi: 10.1137/050626090. |
[3] |
M. Dür and J.-B. Hiriart-Urruty,
Testing copositivity with the help of difference-of-convex optimization, Math. Program., 140 (2013), 31-43.
doi: 10.1007/s10107-012-0625-9. |
[4] |
J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms. I. Fundamentals, Grundlehren der Mathematischen Wissenschaften, 305, Springer-Verlag, Berlin, 1993.
doi: 10.1007/978-3-662-02796-7. |
[5] |
J.-B. Hiriart-Urruty and A. Seeger,
A variational approach to copositive matrices, SIAM Rev., 52 (2010), 593-629.
doi: 10.1137/090750391. |
[6] |
A. Moudafi and P.-E. Maingé,
On the convergence of an approximate proximal method for DC functions, J. Comput. Math., 24 (2006), 475-480.
|
[7] |
J. C. O. Souza, P. R. Oliveira and A. Soubeyran,
Global convergence of a proximal linearized algorithm for difference of convex functions, Optim. Lett., 10 (2016), 1529-1539.
doi: 10.1007/s11590-015-0969-1. |
[8] |
W.-Y. Sun, R. J. B. Sampaio and M. A. B. Candido,
Proximal point algorithm for minimization of DC function, J. Comput. Math., 21 (2003), 451-462.
|
average | min | max | % failure | aver. | min | max | % failure | |
20 | 117 | 78 | 204 | 0 | 111 | 74 | 195 | 0 |
10 | 64 | 32 | 116 | 0 | 58 | 35 | 109 | 0 |
6 | 40 | 24 | 75 | 0 | 36 | 22 | 65 | 0 |
4 | 29 | 17 | 53 | 0 | 23 | 13 | 46 | 0 |
3.5 | 26 | 14 | 49 | 0 | 20 | 12 | 40 | 0 |
3.2365 | 25 | 16 | 43 | 0 | 19 | 11 | 35 | 0 |
$c_n=1.5$ | $c_n=3$ | |||||||
average | min | max | % failure | aver. | min | max | % failure | |
20 | 110 | 74 | 192 | 0 | 108 | 72 | 188 | 0 |
10 | 56 | 33 | 103 | 0 | 54 | 25 | 101 | 0 |
6 | 34 | 20 | 64 | 0 | 32 | 17 | 60 | 0 |
4 | 21 | 13 | 42 | 0 | 19 | 13 | 37 | 0 |
3.5 | 18 | 8 | 34 | 0 | 16 | 9 | 31 | 0.15 |
3.2365 | 16 | 11 | 35 | 16 | 14 | 9 | 28 | 0.17 |
$c_n=5$ | $c_n=40$ | |||||||
average | min | max | % failure | aver. | min | max | % failure | |
20 | 106 | 72 | 187 | 0 | 106 | 71 | 183 | 0 |
10 | 53 | 27 | 100 | 0 | 53 | 24 | 99 | 0 |
6 | 31 | 18 | 58 | 0 | 30 | 17 | 54 | 0 |
4 | 18 | 9 | 32 | 0 | 17 | 10 | 34 | 0 |
3.5 | 15 | 10 | 31 | 12 | 14 | 9 | 28 | 0.15 |
3.2365 | 13 | 9 | 8 | 12 | 12 | 8 | 28 | 0.12 |
average | min | max | % failure | aver. | min | max | % failure | |
20 | 117 | 78 | 204 | 0 | 111 | 74 | 195 | 0 |
10 | 64 | 32 | 116 | 0 | 58 | 35 | 109 | 0 |
6 | 40 | 24 | 75 | 0 | 36 | 22 | 65 | 0 |
4 | 29 | 17 | 53 | 0 | 23 | 13 | 46 | 0 |
3.5 | 26 | 14 | 49 | 0 | 20 | 12 | 40 | 0 |
3.2365 | 25 | 16 | 43 | 0 | 19 | 11 | 35 | 0 |
$c_n=1.5$ | $c_n=3$ | |||||||
average | min | max | % failure | aver. | min | max | % failure | |
20 | 110 | 74 | 192 | 0 | 108 | 72 | 188 | 0 |
10 | 56 | 33 | 103 | 0 | 54 | 25 | 101 | 0 |
6 | 34 | 20 | 64 | 0 | 32 | 17 | 60 | 0 |
4 | 21 | 13 | 42 | 0 | 19 | 13 | 37 | 0 |
3.5 | 18 | 8 | 34 | 0 | 16 | 9 | 31 | 0.15 |
3.2365 | 16 | 11 | 35 | 16 | 14 | 9 | 28 | 0.17 |
$c_n=5$ | $c_n=40$ | |||||||
average | min | max | % failure | aver. | min | max | % failure | |
20 | 106 | 72 | 187 | 0 | 106 | 71 | 183 | 0 |
10 | 53 | 27 | 100 | 0 | 53 | 24 | 99 | 0 |
6 | 31 | 18 | 58 | 0 | 30 | 17 | 54 | 0 |
4 | 18 | 9 | 32 | 0 | 17 | 10 | 34 | 0 |
3.5 | 15 | 10 | 31 | 12 | 14 | 9 | 28 | 0.15 |
3.2365 | 13 | 9 | 8 | 12 | 12 | 8 | 28 | 0.12 |
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