In this paper, using Moore-Penrose inverse, we characterize the feasibility of primal and dual Stein linear programs over symmetric cones in a Euclidean Jordan algebra V. We give sufficient conditions for the solvability of the Stein linear programming problem. Further, we give a characterization of the globally uniquely solvable property for the Stein transformation in terms of a least element of a set in V in the context of the linear complementarity problem. © 2013 World Scientific Publishing Company.

K C Sivakumar

Department of Mathematics

V. Vetrivel

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Stein linear programs over symmetric cones

International Game Theory Review

Let V be a Euclidean Jordan algebra with symmetric cone K. We show that if a linear transformation L on V has the Lipschitzian property and the linear complementarity problem LCP(L,q) over K has a solution for every invertible q∈V, then 〈L(c),c〉&gt;0 for all primitive idempotents c in V. We show that the converse holds for Lyapunov-like transformations, Stein transformations and quadratic representations. We also show that the Lipschitzian Q-property of the relaxation transformation RA on V implies that A is a P-matrix. © 2011 Elsevier Inc. All rights reserved.

Fulltext

Linear Algebra and Its Applications

On the Lipschitzian property in linear complementarity problems over symmetric cones

Positivity

Feasibility and solvability of Lyapunov-type linear programming over symmetric cones

Mathematics of Operations Research

Automorphism Invariance ofP- andGUS-Properties of Linear Transformations on Euclidean Jordan Algebras

Linear Algebra and its Applications

Some P-properties for linear transformations on Euclidean Jordan algebras

On some interconnections between strict monotonicity, globally uniquely solvable, and P properties in semidefinite linear complementarity problems

Journal	International Game Theory Review
ISSN	02191989
Open Access	No