Weighted LCPs and interior point systems for copositive linear transformations on Euclidean Jordan algebras

M. Seetharama Gowda ()
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M. Seetharama Gowda: University of Maryland, Baltimore County

Journal of Global Optimization, 2019, vol. 74, issue 2, No 4, 285-295

Abstract: Abstract In the setting of a Euclidean Jordan algebra V with symmetric cone $$V_+$$ V + , corresponding to a linear transformation M, a ‘weight vector’ $$w\in V_+$$ w ∈ V + , and a $$q\in V$$ q ∈ V , we consider the weighted linear complementarity problem wLCP(M, w, q) and (when w is in the interior of $$V_+$$ V + ) the interior point system IPS(M, w, q). When M is copositive on $$V_+$$ V + and q satisfies an interiority condition, we show that both the problems have solutions. A simple consequence, stated in the setting of $$\mathbb {R}^{n}$$ R n is that when M is a copositive plus matrix and q is strictly feasible for the linear complementarity problem LCP(M, q), the corresponding interior point system has a solution. This is analogous to a well-known result of Kojima et al. on $$\mathbf{P}_*$$ P ∗ -matrices and may lead to interior point methods for solving copositive LCPs.

Keywords: Weighted LCPs; Interior point system; Euclidean Jordan algebra; Degree; Copositive linear transformation; 90C30 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00760-7

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