A Nonmonotone Smoothing-Type Algorithm for a System of Inequalities Associated with Circular Cones

He Huang (), Nuo Qi () and Xin-He Miao
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He Huang: College of Management and Economics, Tianjin University, No. 92, Weijin Road, Tianjin 300072, P. R. China
Nuo Qi: School of Mathematics, Tianjin University, No. 135, Yaguan Road, Tianjin 300350, P. R. China
Xin-He Miao: School of Mathematics, Tianjin University, No. 135, Yaguan Road, Tianjin 300350, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 02, 1-18

Abstract: In this paper, we consider a system of inequalities associated with circular cones. By constructing a new smoothing function, the problem is reformulated as a system of parameterized smooth equations. In addition, we suggest a Newton-type algorithm for solving the smooth equations so that a solution of the problem concerned is found. In particular, the algorithm is proved to be globally and locally quadratically convergent under suitable conditions. The preliminary numerical results demonstrate that the algorithm is effective.

Keywords: System of inequalities; circular cone; smoothing-type algorithm; nonmonotone line search; global convergence (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595922500178

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