This research is funded by a grant under Mathematical Research Impact Centric Support (MATRICS) scheme of Science and Engineering Research Board (SERB), Department of Science & Technology, Govt. of India.
Positive semi-definite matrices arise in various applications in basic sciences, engineering,and operations research. Copositive matrices, semimonotone matrices and other generalizations like P0-matrices of positive semi-definite matrices play a significant role in the theory of linear complementarity problem (LCP). We aim to exploit the LCP theory to further characterize these matrix classes with the motivation that these characterizations will be highly useful not only in optimization theory but also in the applications like block designs, data mining and clustering, a model of energy demand, exchangeable probability distributions, and in dynamical systems and control. We also plan to attempt the interesting open questions in LCP theory like Stone’s conjecture and study the processability of the LCPs with these special matrices by Lemke’s algorithm. As a significant number of applications in economics, physical sciences and engineering lead to either a mathematical programming problem or a game theory problem and LCP provides a unified framework to study many of these problems, the results obtained will be in turn useful in all these areas.