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Properties of some matrix classes based on principal pivot transform

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  • A. K. Das

    (Indian Statistical Institute)

Abstract

In this article, we study the properties of some matrix classes using principal pivot transform (PPT). These matrices with some additional conditions have nonnegative principal minors. We show that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$ Q 0 -property is captured by sufficient matrices introduced by Cottle et al. in (Linear Algebra Appl 114/115:231–249 1989) and the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker stationary points of the corresponding quadratic programming problem. We introduce some more PPT based matrix classes in continuation of (Linear Algebra Appl 400:243–252 2005) and study the properties of these classes.

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  • A. K. Das, 2016. "Properties of some matrix classes based on principal pivot transform," Annals of Operations Research, Springer, vol. 243(1), pages 375-382, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-014-1622-6
    DOI: 10.1007/s10479-014-1622-6
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    References listed on IDEAS

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    1. S. R. Mohan & T. Parthasarathy & R. Sridhar, 1994. "The Linear Complementarity Problem with Exact Order Matrices," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 618-644, August.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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