The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Global Lipschitz Continuity of Solutions to Parameterized Variational Inequalities

Antonino Maugeri; Laura Scrimali

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 1, page 45-69
  • ISSN: 0392-4041

How to cite

top

Maugeri, Antonino, and Scrimali, Laura. "Global Lipschitz Continuity of Solutions to Parameterized Variational Inequalities." Bollettino dell'Unione Matematica Italiana 2.1 (2009): 45-69. <http://eudml.org/doc/290590>.

@article{Maugeri2009,
author = {Maugeri, Antonino, Scrimali, Laura},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {45-69},
publisher = {Unione Matematica Italiana},
title = {Global Lipschitz Continuity of Solutions to Parameterized Variational Inequalities},
url = {http://eudml.org/doc/290590},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Maugeri, Antonino
AU - Scrimali, Laura
TI - Global Lipschitz Continuity of Solutions to Parameterized Variational Inequalities
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/2//
PB - Unione Matematica Italiana
VL - 2
IS - 1
SP - 45
EP - 69
LA - eng
UR - http://eudml.org/doc/290590
ER -

References

top
  1. ARÓS, A. - SOFONEA, M. - VIAÑO, J. M., A class of evolutionary variational inequalities with Volterra-type term, Math. Models Methods Appl. Sci., 14, No. 4 (2004), 557-577. Zbl1077.74035MR2046578DOI10.1142/S0218202504003350
  2. BARBAGALLO, A., Regularity results for evolutionary nonlinear variational and quasi-variational inequalities with applications to dynamic equilibrium problems, J. Global Optim., 40, No. 1-3 (2008). Zbl1149.49032MR2373537DOI10.1007/s10898-007-9194-5
  3. BOLTZMANN, L., Zur Theorie der elastischen Nachwirkung, Sitzber. Kaiserl. Akad. Wiss. Wien, Math.-Naturw. Kl., 70, Sect. II (1874), 275-300. 
  4. BECKMAN, M. J. - WALLACE, J. P., Continuous lags and the stability of market equilibrium, Economica, New Series, 36, No. 141 (1969), 58-68. 
  5. BOLTZMANN, L., Zur Theorie der elastischen Nachwirkung, Ann. Phys. u. Chem., 5 (1878), 430-432. Zbl10.0670.01
  6. BONNANS, J. F. - SHAPIRO, A., Perturbation analysis of optimization problems, Springer, New York (2000). Zbl0966.49001MR1756264DOI10.1007/978-1-4612-1394-9
  7. COLEMAN, B. D. - NOLL, W., Foundations of linear viscoelasticity, Rev. of Modern Physics, 33, No. 2 (1961), 239-249. Zbl0103.40804MR158605DOI10.1103/RevModPhys.33.239
  8. DANIELE, P. - MAUGERI, A. - OETTLI, W., Time-dependent traffic equilibria, J. Optim. Theory Appl., 103, No. 3 (1999), 543-554. Zbl0937.90005MR1727254DOI10.1023/A:1021779823196
  9. DANIELE, P. - MAUGERI, A., Variational inequalities and discrete and continuum models of network equilibrium problems, Math. Comput. Model., 35 (2002), 689-708. Zbl0994.90033MR1884027DOI10.1016/S0895-7177(02)80030-9
  10. P. DANIELE - F. GIANNESSI - A. MAUGERI (Eds.), Equilibrium problems and variational models, Kluwer Academic Publishers (2003). MR2026132DOI10.1007/0-306-48026-3_12
  11. DANIELE, P., Dynamic networks and evolutionary variational inequalities, Edward Elgar Publishing (2006). Zbl1117.49002MR2273417
  12. DANIELE, P. - GIUFFRÈ, S., General infinite dimensional duality and applications to evolutionary network equilibrium problems, Optim. Lett., 1, No. 3 (2007), 227-243. Zbl1151.90577MR2340691DOI10.1007/s11590-006-0028-z
  13. DANIELE, P. - GIUFFRÈ, S. - IDONE, G. - MAUGERI, A., Infinite dimensional duality and applications, Math. Ann., 339, No. 1 (2007), 221-239. Zbl1356.49064MR2317768DOI10.1007/s00208-007-0118-y
  14. FACCHINEI, F. - PANG, J. S., Finite-dimensional variational inequalities and complementarity problems, Springer, New York (2003). Zbl1062.90001MR1955649
  15. FIACCO, A. V. - MCCORMICK, G. P., Nonlinear programming: sequential unconstrained minimization techniques, Wiley, New York (1968). Zbl0193.18805MR243831
  16. FIACCO, A. V., Sensitivity analysis for nonlinear programming using penality methods, Math. Program., 10 (1976), 287-311. Zbl0357.90064MR434444DOI10.1007/BF01580677
  17. FIACCO, A. V., An introduction to sensitivity and stability analysis in Nonlinear programming, Academic Press, New York (1983). Zbl0543.90075MR721641
  18. FICHERA, G., Integro-differential problems of hereditary elasticity, Atti Sem. Mat. Fis. Univ. Modena, XXVI (1977), 363-370. Zbl0407.73005MR532388
  19. F. GIANNESSI - A. MAUGERI (Eds.), Variational inequalities and network equilibrium problems, Plenum Publishing, New York (1995). MR1331396DOI10.1007/978-1-4899-1358-6
  20. F. GIANNESSI - A. MAUGERI - P. PARDALOS (Eds.), Equilibrium problems: non-smooth optimization and variational inequality models, Kluwer Academic Publishers, Dordrecht, The Netherlands (2001). MR2030621
  21. GIANNESSI, F. - MAUGERI, A., Preface [Special issue on the Proeceedings of the First AMS-UMI Joint Meeting], J. Global Optim., 28, No. 3-4 (2004). MR2072682DOI10.1023/B:JOGO.0000026452.32070.99
  22. F. GIANNESSI - A. MAUGERI (Eds.), Variational inequalities and applications, Springer, New York (2005). 
  23. GWINNER, J., Time-dependent variational inequalities. Some recent trends. In Daniele P., Giannessi F. and Maugeri A. (Eds.), Equilibrium problems and variational models, Academic Publishers, Dordrecht, The Netherlands (2003), 225-264. Zbl1069.49005MR2043474DOI10.1007/978-1-4613-0239-1_12
  24. HEINONEN, J., Lectures on Lipschitz analysis. In Lectures at the 14th Jyväskylä Summer School (August, 2004). Zbl1086.30003MR2177410
  25. JAHN, J., Introduction to the theory of nonlinear optimization, Springer-Verlag, Berlin, Germany (1996). Zbl0855.49001MR1429391DOI10.1007/978-3-662-03271-8
  26. KINDERLEHER, D. - STAMPACCHIA, G., An introduction to variational inequalities and their applications, Academic Press, New York (1980). MR567696
  27. KYPARISIS, J., Uniqueness and differentiability of solutions of parametric nonlinear complementarity problems, Math. Program., 36 (1986), 105-113. Zbl0613.90096MR862072DOI10.1007/BF02591993
  28. KYPARISIS, J., Solution differentiability for variational inequalities, Math. Program., 48 (1990), 285-301. Zbl0727.90082MR1073712DOI10.1007/BF01582260
  29. KYPARISIS, J., Sensitivity analysis for variational inequalities and nonlinear complementarity problems, Ann. Oper. Res., 27 (1990), 143-174. Zbl0723.90075MR1088991DOI10.1007/BF02055194
  30. LIONS, J. L. - STAMPACCHIA, G., Variational inequalities, Comm. Pure Appl. Math., 22 (1967) 493-519. MR216344DOI10.1002/cpa.3160200302
  31. MAUGERI, A., Variational and quasi-variational inequalities and applications to optmization problems in networks, Boll. Un. Mat. Ital. B, 7, No. 4 (1990), 327-343. Zbl0705.90023MR1061221
  32. MAUGERI, A., Dynamic Models and generalized equilibrium problems. In Giannessi F. (Ed.), New Trends in Mathematical Programming, Kluwer Academic Publishers (1998), 191-202. Zbl0908.90120MR1641319DOI10.1007/978-1-4757-2878-1_15
  33. MAUGERI, A. - VITANZA, C., Time-dependent equilibrium problems. In Migdalos A., Pardalos P. and Pitsoulis L. (Eds.), Pareto Optimality Game Theory and Equilibria, Springer (2008), 505-524. Zbl1191.49009MR2441391DOI10.1007/978-0-387-77247-9_10
  34. MORDUKHOVICH, B., Variational analysis and generalized differentiation (Springer-Verlag , 2006). MR2191745
  35. QUI, Y. - MAGNANTI, T. L., Sensitivity analysis for variational inequalities, Math. Oper. Res., 17 (1992), 61-76. Zbl0756.49009MR1148778DOI10.1287/moor.17.1.61
  36. ROBINSON, S. M., Some continuity properties of polyhedral multifunctions, Math. Programming Stud., 14 (1981), 206-214. Zbl0449.90090MR600130DOI10.1007/bfb0120929
  37. ROBINSON, S. M., Generalized equations and their solutions, part II: applications to nonlinear programming, Math. Programming Stud., 19 (1982), 200-221. Zbl0495.90077MR669732DOI10.1007/bfb0120989
  38. ROBINSON, S. M., Implicit B-Differentiability in generalized equations, Technical Summary Report 2854, Mathematics Research center, University of Wisconsin, Madison, WI (1985). 
  39. ROBINSON, S. M. - LU, S., Solution continuity in variational conditions, J. Global Optim., 40, No. 1-3 (2008). Zbl1145.90096MR2373568DOI10.1007/s10898-007-9192-7
  40. SCRIMALI, L., Quasi-variational inequalities in transportation networks, Math. Models Methods Appl. Sci., 14, No. 10 (2004), 1541-1560. Zbl1069.90026MR2095302DOI10.1142/S0218202504003714
  41. SCRIMALI, L., The financial equilibrium problem with implicit budget constraints, Cent. Eur. J. Oper. Res., 16, No. 2 (2008), 191-203. Zbl1145.91028MR2407047DOI10.1007/s10100-007-0046-7
  42. SCRIMALI, L., A solution differentiability result for evolutionary quasi-variational inequalities, J. Global Optim., 40, No. 1-3 (2008). Zbl1282.49008MR2373569DOI10.1007/s10898-007-9189-2
  43. SHAPIRO, A., Sensitivity analysis of nonlinear programs and differentiability properties of metric projections, SIAM J. Control Optim., 26 (1988), 628-645. Zbl0647.90089MR937676DOI10.1137/0326037
  44. SHAPIRO, A., Sensitivity analysis of parameterized variational inequalities, Math. Oper. Res., 30, No. 1 (2005), 109-126. Zbl1082.49015MR2125140DOI10.1287/moor.1040.0115
  45. SMITH, M. J., A new dynamic traffic model and the existence and calculation of dynamic user equilbria on congested capacity-constrained road networks, Transportation Res. B, 27B, No. 1 (1993), 49-63. 
  46. STEINBACH, J., On a variational inequality containing a memory term with an application in electro-chemical machining, J. Convex Anal., 5, No. 1 (1998), 63-80. Zbl0908.49011MR1649441
  47. STEINBACH, J., A variational inequality approach to free boundary problems with applications in mould filling (Birkhäuser-Verlag, 2002). Zbl1011.35001MR1891393DOI10.1007/978-3-0348-7597-4
  48. VOLTERRA, V., Sulle equazioni integro-differenziali della teoria della elasticità, Rend. Acc. Naz. Lincei, XVIII, No. 2 (1909), 295-301. Zbl40.0870.01
  49. VOLTERRA, V., Sulle equazioni integro-differenziali della elasticità nel caso della entropia, Rend. Acc. Naz. Lincei, XVIII, No. 2 (1909), 577-586. Zbl40.0871.01
  50. VOLTERRA, V., Sur les equation intégro-differentielles et leurs applications, Acta Math., XXXV (1912), 295-356. Zbl43.0431.03MR1555080DOI10.1007/BF02418820
  51. WARDROP, J. G., Some theoretical aspects of road traffic research. In Proceedings of the Institute of Civil Engineers, Part II (1952), 325-378). 
  52. YEN, N. D., Hölder continuity of solutions to a parametric variational inequality, Appl. Math. Optim., 31 (1995), 245-255. MR1316259DOI10.1007/BF01215992
  53. YEN, N. D., Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint, Math. Oper. Res., 20 (1995), 695-708. Zbl0845.90116MR1354777DOI10.1287/moor.20.3.695

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.