#### Date of Submission

2-28-1998

#### Date of Award

2-28-1999

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Mathematics

#### Department

SQC and OR Unit (Bangalore)

#### Supervisor

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, wÎ£Rn, 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.

#### Control Number

ISILib-TH42

#### Creative Commons License

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

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Hohan, S. Dr., "Linear Complementarity Problem with a Z Matrix." (1999). *Doctoral Theses*. 414.

https://digitalcommons.isical.ac.in/doctoral-theses/414

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843804