Smoothing inexact Newton method based on a new derivative-free nonmonotone line search for the NCP over circular cones

Jingyong Tang () and Jinchuan Zhou ()
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Jingyong Tang: Xinyang Normal University
Jinchuan Zhou: Shandong University of Technology

Annals of Operations Research, 2020, vol. 295, issue 2, No 12, 787-808

Abstract: Abstract In this paper we consider the nonlinear complementarity problem over circular cones (CCNCP) which contains a lot of circular cone optimization problems. We study a one-parametric class of smoothing functions which can be used to reformulate the CCNCP as a system of smooth nonlinear equations. Based on the equivalent reformulation, we propose a smoothing inexact Newton method to solve the CCNCP. In each iteration, the proposed method solves the nonlinear equations only approximately. Since the inexact direction is not necessarily descent, a new derivative-free nonmonotone line search is developed to ensure that the proposed method has global and local superlinear and quadratical convergence. Some numerical results are also reported.

Keywords: Nonlinear complementarity problem; Circular cones; Smoothing function; Inexact Newton method; Superlinear/quadratical convergence (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-020-03773-8

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