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Superlinearly convergent smoothing Newton continuation algorithms for variational inequalities over definable sets

Chek Beng Chua(cbchua***at***ntu.edu.sg)
Le Thi Khanh Hien(TKLE1***at***e.ntu.edu.sg)

Abstract: In this paper, we use the concept of barrier-based smoothing approximations introduced by Chua and Li to extend various smoothing Newton continuation algorithms to variational inequalities over general closed convex sets X. We prove that when the underlying barrier has a gradient map that is definable in some o-minimal structure, the iterates generated converge superlinearly to a solution of the variational inequality. We further prove that if X is proper and definable in the o-minimal structure ℜ_{an}^{ℜ_{alg}}, then the gradient map of its universal barrier is definable in the o-minimal expansion ℜ_{an,exp}.

Keywords: variational inequalities, smoothing Newton continuation, superlinear convergence, barrier-based smoothing approximation.

Category 1: Complementarity and Variational Inequalities

Citation: Research Report, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, February 2014.

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Entry Submitted: 02/17/2014
Entry Accepted: 02/18/2014
Entry Last Modified: 02/17/2014

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