zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stable pseudomonotone variational inequality in reflexive Banach spaces. (English) Zbl 1124.49005
Summary: Stability of a generalized variational inequality with either the mapping or the set perturbed is discussed in reflexive Banach spaces, provided that the mappings are pseudomonotone in the sense of Karamardian. As a byproduct, generalized variational inequality having nonempty and bounded set is proved to be equivalent to the strictly feasibility.

MSC:
49J40Variational methods including variational inequalities
49K40Sensitivity, stability, well-posedness of optimal solutions
WorldCat.org
Full Text: DOI
References:
[1] Minty, G. J.: On the generalization of a direct method of the calculus of variations. Bull. amer. Math. soc. 73, 315-321 (1967) · Zbl 0157.19103
[2] Browder, F. E.: Nonlinear maximal monotone operators in Banach space. Math. ann. 175, 89-113 (1968) · Zbl 0159.43901
[3] Konnov, I. V.: On quasimonotone variational inequalities. J. optim. Theory appl. 99, No. 1, 165-181 (1998) · Zbl 0911.90325
[4] Liu, J.: Sensitivity analysis in nonlinear programs and variational inequalities via continuous selections. SIAM J. Control optim. 33, No. 4, 1040-1060 (1995) · Zbl 0839.49017
[5] Ha, C. D.: Application of degree theory in stability of the complementarity problem. Math. oper. Res. 12, No. 2, 368-376 (1987) · Zbl 0616.90082
[6] Dafermos, S.: Sensitivity analysis in variational inequalities. Math. oper. Res. 13, No. 3, 421-434 (1988) · Zbl 0674.49007
[7] Kyparisis, J.: Parametric variational inequalities with multivalued solution sets. Math. oper. Res. 17, No. 2, 341-364 (1992) · Zbl 0777.49008
[8] Qiu, Y.; Magnanti, T. L.: Sensitivity analysis for variational inequalities. Math. oper. Res. 17, No. 1, 61-76 (1992) · Zbl 0756.49009
[9] Tobin, R. L.: Sensitivity analysis for variational inequalities. J. optim. Theory appl. 48, No. 1, 191-209 (1986) · Zbl 0557.49004
[10] Gowda, M. S.; Pang, J. -S.: Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory. Math. oper. Res. 19, No. 4, 831-879 (1994) · Zbl 0821.90114
[11] Noor, M. A.: Sensitivity analysis for quasi-variational inequalities. J. optim. Theory appl. 95, No. 2, 399-407 (1997) · Zbl 0896.49003
[12] Noor, M. A.: Sensitivity analysis for variational inequalities. Optimization 41, No. 3, 207-217 (1997) · Zbl 0887.49007
[13] Noor, M. A.; Noor, K. I.: Sensitivity analysis for quasi-variational inclusions. J. math. Anal. appl. 236, No. 2, 290-299 (1999) · Zbl 0949.49007
[14] Noor, M. A.: Some developments in general variational inequalities. Appl. math. Comput. 152, No. 1, 199-277 (2004) · Zbl 1134.49304
[15] Mclinden, L.: Stable monotone variational inequalities. Math. programming 48, No. 2 (Ser. B), 303-338 (1990) · Zbl 0726.90093
[16] Adly, S.; Théra, M.; Ernst, E.: Stability of the solution set of non-coercive variational inequalities. Commun. contemp. Math. 4, No. 1, 145-160 (2002) · Zbl 1012.47052
[17] Karamardian, S.: Complementarity problems over cones with monotone and pseudomonotone maps. J. optim. Theory appl. 18, No. 4, 445-454 (1976) · Zbl 0304.49026
[18] Auslender, A.; Correa, R.: Primal and dual stability results for variational inequalities. Comput. optim. Appl. 17, No. 2 -- 3, 117-130 (2000) · Zbl 0987.90077
[19] Aubin, J. P.: Optima and equilibria. (1993)
[20] Rockafellar, R. T.: Convex analysis. (1970) · Zbl 0193.18401
[21] Zălinescu, C.: Convex analysis in general vector spaces. (2002) · Zbl 1023.46003
[22] He, Y. R.; Ng, K. F.: Strict feasibility of generalized complementarity problems. J. austral. Math. soc., ser A 81, No. 1, 15-20 (2006) · Zbl 1170.90498
[23] He, Y. R.: A relationship between pseudomonotone and monotone mappings. Appl. math. Lett. 17, No. 4, 459-461 (2004) · Zbl 1060.49004
[24] Daniilidis, A.; Hadjisavvas, N.: On the subdifferentials of quasiconvex and pseudoconvex functions and cyclic monotonicity. J. math. Anal. appl. 237, No. 1, 30-42 (1999) · Zbl 0934.49015
[25] Daniilidis, A.; Hadjisavvas, N.: Coercivity conditions and variational inequalities. Math. programming 86, No. 2 (Ser. A), 433-438 (1999) · Zbl 0937.49003
[26] Fan, K.: A generalization of tychonoff’s fixed point theorem. Math. ann. 142, 305-310 (1961) · Zbl 0093.36701
[27] Crouzeix, J. -P.: Pseudomonotone variational inequality problems: existence of solutions. Math. programming 78, No. 3 (Ser. A), 305-314 (1997) · Zbl 0887.90167
[28] Flores-Bazán, F.: Existence theorems for generalized noncoercive equilibrium problems: the quasi-convex case. SIAM J. Optim. 11, No. 3, 675-690 (2000) · Zbl 1002.49013
[29] Daniilidis, A.; Hadjisavvas, N.: Characterization of nonsmooth semistrictly quasiconvex and strictly quasiconvex functions. J. optim. Theory appl. 102, No. 3, 525-536 (1999) · Zbl 1010.49013
[30] Sion, M.: On general minimax theorems. Pacific J. Math. 8, 171-176 (1958) · Zbl 0081.11502