Error Bounds for the Solution Sets of Quadratic Complementarity Problems

Shenglong Hu (), Jie Wang () and Zheng-Hai Huang ()
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Shenglong Hu: Hangzhou Dianzi University
Jie Wang: China Jiliang University
Zheng-Hai Huang: Tianjin University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 12, 983-1000

Abstract: Abstract In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standard violation measure of the polynomial equalities and inequalities. These fractional local error bounds are given with explicit exponents. A fractional local error bound with an explicit exponent via the natural residual function is new in the tensor/polynomial complementarity problems literature. The other fractional local error bounds take into account the sparsity structures, from both the algebraic and the geometric perspectives, of the third-order tensor in a quadratic complementarity problem. They also have explicit exponents, which improve the literature significantly.

Keywords: Error bound; Quadratic complementarity problem; Polynomial system; 90C33; 15A69 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-018-1356-8

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