Computing minimum norm solution of a specific constrained convex nonlinear problem
Saeed Ketabchi; Hossein Moosaei
Kybernetika (2012)
- Volume: 48, Issue: 1, page 123-129
- ISSN: 0023-5954
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topKetabchi, Saeed, and Moosaei, Hossein. "Computing minimum norm solution of a specific constrained convex nonlinear problem." Kybernetika 48.1 (2012): 123-129. <http://eudml.org/doc/246216>.
@article{Ketabchi2012,
abstract = {The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties.},
author = {Ketabchi, Saeed, Moosaei, Hossein},
journal = {Kybernetika},
keywords = {solution set of convex problems; alternative theorems; minimum norm solution; residual vector; solution set of convex problems; alternative theorems; minimum norm solution; residual vector},
language = {eng},
number = {1},
pages = {123-129},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Computing minimum norm solution of a specific constrained convex nonlinear problem},
url = {http://eudml.org/doc/246216},
volume = {48},
year = {2012},
}
TY - JOUR
AU - Ketabchi, Saeed
AU - Moosaei, Hossein
TI - Computing minimum norm solution of a specific constrained convex nonlinear problem
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 1
SP - 123
EP - 129
AB - The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties.
LA - eng
KW - solution set of convex problems; alternative theorems; minimum norm solution; residual vector; solution set of convex problems; alternative theorems; minimum norm solution; residual vector
UR - http://eudml.org/doc/246216
ER -
References
top- L. Armijo, 10.2140/pjm.1966.16.1, Pacific J. Math. 16 (1966), 1-3. (1966) MR0191071DOI10.2140/pjm.1966.16.1
- Yu. G. Evtushenko, A. I. Golikov, New perspective on the theorems of alternative., In: High Performance Algorithms and Software for Nonlinear Optimization, Kluwer Academic Publishers B.V., 2003, pp. 227-241. (2003) Zbl1044.90088MR2040365
- A. I. Golikov, Yu. G. Evtushenko, Theorems of the alternative and their applications in numerical methods., Comput. Math. and Math. Phys. 43 (2003), 338-358. (2003) MR1993755
- C. Kanzow, H. Qi, L. Qi, 10.1023/A:1022457904979, J. Optim. Theory Appl. 116 (2003), 333-345. (2003) Zbl1043.90046MR1967673DOI10.1023/A:1022457904979
- S. Ketabchi, E. Ansari-Piri, 10.1016/j.cam.2006.07.004, J. Comput. Appl. Math. 206 (2007), 288-292. (2007) Zbl1131.90042MR2337444DOI10.1016/j.cam.2006.07.004
- O. L. Magasarian, 10.1016/0167-6377(88)90047-8, Oper. Res. Lett. 7 (1988), 21-26. (1988) MR0936347DOI10.1016/0167-6377(88)90047-8
- O. L. Magasarian, 10.1023/B:JOTA.0000026128.34294.77, J. Optim. Theory Appl. 121 (2004), 1-18. (2004) MR2062967DOI10.1023/B:JOTA.0000026128.34294.77
- O. L. Magasarian, 10.1080/1055678021000028375, Optim. Meth. Software 17 (2002), 913-930. (2002) MR1953825DOI10.1080/1055678021000028375
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