On the construction of gap functions for variational inequalities via conjugate duality. (English) Zbl 1141.49303
Summary: We deal with the construction of gap functions for variational inequalities by using an approach which bases on the conjugate duality. Under certain assumptions we also investigate a further class of gap functions for the variational inequality problem, the so-called dual gap functions.
MSC:
| 49J40 | Variational inequalities |
References:
| [1] | DOI: 10.1080/01630568908816335 · Zbl 0678.49010 · doi:10.1080/01630568908816335 |
| [2] | Auslender A., Optimisation: Méthods Numériques (1976) |
| [3] | DOI: 10.1006/jmaa.1997.5608 · Zbl 0945.49004 · doi:10.1006/jmaa.1997.5608 |
| [4] | Ekeland I., Convex Analysis and Variational Problems (1976) · Zbl 0322.90046 |
| [5] | Facchinei F., Springer Series in Operations Research, in: Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) |
| [6] | DOI: 10.1007/BF01585696 · Zbl 0756.90081 · doi:10.1007/BF01585696 |
| [7] | DOI: 10.1007/978-1-4899-0289-4_11 · doi:10.1007/978-1-4899-0289-4_11 |
| [8] | DOI: 10.1007/BF02032131 · Zbl 0844.90069 · doi:10.1007/BF02032131 |
| [9] | DOI: 10.1201/9781420018868 · doi:10.1201/9781420018868 |
| [10] | DOI: 10.1007/BF01582255 · Zbl 0734.90098 · doi:10.1007/BF01582255 |
| [11] | DOI: 10.1016/0167-6377(82)90049-9 · Zbl 0486.90070 · doi:10.1016/0167-6377(82)90049-9 |
| [12] | Kinderlehrer Dr., Pure and Applied Mathematics 88, in: An Introduction to Variational Inequalities and Their Applications (1980) |
| [13] | DOI: 10.1155/S1110757X02106012 · Zbl 1029.47043 · doi:10.1155/S1110757X02106012 |
| [14] | DOI: 10.1007/BF01582565 · Zbl 0819.65101 · doi:10.1007/BF01582565 |
| [15] | DOI: 10.1137/S1052623496309867 · Zbl 1032.90050 · doi:10.1137/S1052623496309867 |
| [16] | Peng J. M., Mathematical Programming A 78 pp 347– |
| [17] | DOI: 10.1016/0362-546X(92)90125-X · Zbl 0768.49008 · doi:10.1016/0362-546X(92)90125-X |
| [18] | DOI: 10.1137/1.9781611970524 · doi:10.1137/1.9781611970524 |
| [19] | DOI: 10.1023/A:1022660704427 · Zbl 0879.90180 · doi:10.1023/A:1022660704427 |
| [20] | DOI: 10.1023/A:1022422407705 · Zbl 1027.49004 · doi:10.1023/A:1022422407705 |
| [21] | DOI: 10.1007/s00245-003-0771-9 · Zbl 1048.49007 · doi:10.1007/s00245-003-0771-9 |
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