Regularized Nonconvex Mixed Variational Inequalities: Auxiliary Principle Technique and Iterative Methods

Javad Balooee ()
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Javad Balooee: Islamic Azad University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 3, No 4, 774-801

Abstract: Abstract In this paper, we turn our attention to formulating and studying a new class of variational inequalities in a nonconvex setting, called regularized nonconvex mixed variational inequalities. By using the auxiliary principle technique, some new predictor corrector methods for solving such class of regularized nonconvex mixed variational inequalities are suggested and analyzed. The study of convergence analysis of the proposed iterative algorithms requires either pseudomonotonicity or partially mixed relaxed and strong monotonicity of the operator involved in regularized nonconvex mixed variational inequalities. As a consequence of our main results, we provide the correct versions of the algorithms and results presented in the literature.

Keywords: Regularized nonconvex mixed variational inequalities; Auxiliary principle technique; Prox-regularity; Nonconvex sets; Predictor–corrector methods; Convergence analysis; 47H05; 47J20; 47J25; 49J40; 65K10; 65K15 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1046-3

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