Noncoercive Variational–Hemivariational Inequalities: Existence, Approximation by Double Regularization, and Application to Nonmonotone Contact Problems

Ouayl Chadli (), Joachim Gwinner () and M. Zuhair Nashed ()
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Ouayl Chadli: Ibn Zohr University
Joachim Gwinner: Universität der Bundeswehr München
M. Zuhair Nashed: University of Central Florida

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 4, 42-65

Abstract: Abstract We study noncoercive nonlinear variational–hemivariational inequalities that encompass semicoercive nonlinear monotone variational inequalities and pseudomonotone variational inequalities in reflexive Banach spaces, respectively, hemivariational inequalities in function spaces. We present existence and approximation results. Our approach consists in a double regularization: we combine a Browder–Tikhonov regularization with regularization tools of nondifferentiable optimization to smooth the jumps in the hemivariational term. As application, we treat a noncoercive unilateral contact problem in continuum mechanics with nonmonotone friction.

Keywords: Nonlinear variational–hemivariational inequality; Noncoercivity; Pseudomonotone bifunction; Browder–Tikhonov regularization; Plus function; Regularization by smoothing; Unilateral contact problem; Nonmonotone friction; 49J40; 49J52; 35J87; 74M10 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02006-1

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