Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



SQC and OR Unit (Bangalore)


Ramamurthy, K. G. (SQCOR-Bangalore; ISI)

Abstract (Summary of the Work)

A square mtrix M whose off dingonal clements are nonpositivo is known as a Z-a trix. 2-n trices and their genernlisations known na L mtricca have been used in interindustry models by Leantief and Gale. Yoro recently 2-un trices tave bcen congiderered in the contexts of aomo operationl resoarch problena auoh aa the minimu ooet maltifaoility inventory eystous and reaouroe allocation.Given a square matrix M of order n and a vector q in 1", the problem of finding nornogn tive solutions in the variables w11s,i= 1,2, ...., n and '8, 1= 1,2, ....., n to the system of equationsw - Mz =q, wΣRn, z(-Rn is known as the linear complenentarity problem. This problem has been shown to be a unified form of mny probleme a rise in mathemtical programing, gane theory, structural engineering and fluid mechanics,In this dissertation we consider the above linear complementority problem with N as a 2-matrix. A problem of fluid mechanics can be Cormalated as a linear componentarily problem with Mae a 2-matrix. More generally such probleme occur in the dissertation of elliptic partial differential equations.Chapter 1 provides a general introduction to the linear complementarity problem and reviews the relevant resulte on this problem and on 2-matrices. Our results on the linear complenentarity problem with a 2-matrix are presented in chaptera 2,3 and 4. sumery of those reaults. In section 1.7 we prosont a chapterwise.


ProQuest Collection ID:

Control Number


Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.