Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-16T09:36:53.475Z Has data issue: false hasContentIssue false
  • English
  • Français

A linear complementarity problem involving a subgradient

Published online by Cambridge University Press:  17 April 2009

J. Parida ,
A. Sen  and
A. Kumar
J. Parida
Affiliation:
Department of Mathematics, Regional Engg. College, Rourkela 769008, India
A. Sen
Affiliation:
Lecturer in Mathematics, Vedvyas College, Rourkela - 769041, India
A. Kumar
Affiliation:
Lecturer in Mathematics, SKDAV Women's College, Rourkela, India
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A linear complementarity problem, involving a given square matrix and vector, is generalised by including an element of the subdifferential of a convex function. The existence of a solution to this nonlinear complementarity problem is shown, under various conditions on the matrix. An application to convex nonlinear nondifferentiable programs is presented.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 345 - 351
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Berman, A., ‘Matrices and the linear complementarity problem’, Linear Algebra Appl. 40 (1981), 249–256.CrossRefGoogle Scholar
[2]Eaves, B.C., ‘The linear complementartiy problem’, Management Sci. 17 (1971), 612–634.CrossRefGoogle Scholar
[3]Karamardian, S., ‘The complementarity problem’, Math. Programming 2 (1972), 107–129.CrossRefGoogle Scholar
[4]McLinden, L., ‘The complementarity problem for maximal monotone mnultifunctions’, in Variational Inequalities and Complementarity Problems, ed. Cottle, R.W., Gianessi, F. and Lions, J.L., pp. 251–270 (John Wiley and Sons, Chichester, 1980).Google Scholar
[5]Mond, B., ‘A class of nondifferentiable mathematical programming problems’, J. Math. Anal. Appl. 46 (1974), 169–174.CrossRefGoogle Scholar
[6]Mond, B. and Schecter, M., ‘A programming problem with an Lp norm in the objective function’, J. Austral. Math. Soc. Ser. B 19 (1976), 333–342.CrossRefGoogle Scholar
[7]Parida, J. and Sen, A., ‘Duality and existence theory for nondifferentiable programnling’, J. Optim. Theory Appl. 48 (1986), 451–458.CrossRefGoogle Scholar
[8]Parida, J. and Sen, A., ‘A class of nonlinear complementarity problem for multifunctions’, J. Optim. Thoery Appl. 53 (1987), 105–113.CrossRefGoogle Scholar
[9]Rockafellar, R.T., Convex Analysis (Princeton University Press, Princeton, New Jersey, 1969).Google Scholar
[10]Schechter, M., ‘A subgradient duality theorem’, J. Math. Anal. Appl. 81 (1977), 850–855.CrossRefGoogle Scholar