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Positive definite and Gram tensor complementarity problems

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Abstract

Given a continuous function and , the non-linear complementarity problem \(\text{ NCP }(g,q)\) is to find a vector such that

$$\begin{aligned} x \ge 0,~~y:=g(x) +q\ge 0~~\text{ and }~~x^Ty=0. \end{aligned}$$

We say that g has the Globally Uniquely Solvable (\(\text{ GUS }\))-property if \(\text{ NCP }(g,q)\) has a unique solution for all and C-property if \(\mathrm{NCP}(g,q)\) has a convex solution set for all . In this paper, we find a class of non-linear functions that have the \(\text{ GUS }\)-property and C-property. These functions are constructed by some special tensors which are positive semidefinite. We call these tensors as Gram tensors.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology-Madras, Chennai, India

    R. Balaji & K. Palpandi

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  1. R. Balaji
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  2. K. Palpandi
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Correspondence to K. Palpandi.

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Balaji, R., Palpandi, K. Positive definite and Gram tensor complementarity problems. Optim Lett 12, 639–648 (2018). https://doi.org/10.1007/s11590-017-1188-8

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  • DOI: https://doi.org/10.1007/s11590-017-1188-8

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