×

A complementarity problem in mathematical programming in Banach space. (English) Zbl 0547.90099

An existence and uniqueness theorem for the nonlinear complementarity problem over arbitrary closed convex cones in a reflexive real Banach space is established. The same result has been proved by Bazaraa, Goode and Nashed under different assumptions. This theorem contains the result obtained by Nanda as a particular case.
Reviewer: Ying Meiqian

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C48 Programming in abstract spaces
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bazaraa, M.S; Goode, J.J; Nashed, M.Z, A nonlinear complementarity problem in mathematical programming in Banach space, (), 165-170, (1) · Zbl 0303.47039
[2] Eaves, B.C, On the basic theorem of complementarity, Math. programming, 1, 68-75, (1971) · Zbl 0227.90044
[3] Karamardian, S; Karamardian, S, The nonlinear complementarity problem with applications, II, J. optim. theory appl., J. optim. theory appl., 4, 167-181, (1969) · Zbl 0169.51302
[4] Karamardian, S, Generalised complementarity problem, J. optim. theory appl., 8, 161-168, (1971) · Zbl 0218.90052
[5] Mosco, U, Convergence of convex sets and solutions of variational inequalities, Adv. in math., 3, 520-585, (1969) · Zbl 0192.49101
[6] Nanda, Sribatsa; Nanda, Sudarsan, A complex nonlinear complementarity problem, Bull. austral. math. soc., 19, 437-444, (1978) · Zbl 0417.90084
[7] Nanda, Sribatsa; Nanda, Sudarsan, On stationary points and the complementarity problem, Bull. austral. math. soc., 20, 77-86, (1979) · Zbl 0404.90094
[8] Nanda, Sribatsa; Nanda, Sudarsan, A nonlinear complementarity problem in mathematical programming in Hilbert space, Bull. austral. math. soc., 20, 233-236, (1979) · Zbl 0404.90091
[9] Nanda, Sribatsa; Nanda, Sudarsan, A nonlinear complementarity problem in Banach space, Bull. austral. math. soc., 21, 351-356, (1980) · Zbl 0424.49002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.