JERAJournal of Electronic Research and Application2208-35022208-3510Bio-Byword Scientific Publishing Pty. Ltd.10.26689/jera.v10i4.14895ArticleNew Iterative Methods for Solving Exponentially General Regularized Nonconvex Variational Inequalityhttps://artdesignp.com/journal/JERA/10/4/10.26689/jera.v10i4.14895ZhangSiyu,YaoSisheng20261042026-05-21In this paper, we introduce and study a new class of extended exponentially general regularized nonconvex variational inequalities. We showed that the inequalities are equivalent to fixed-point problems through the use of the projection properties. Based on this equivalence, we discuss the existence and uniqueness of solutions to the extended exponentially general regularized nonconvex variational inequalities. We present a new self-adaptive finite p-step iterative projection scheme that uses multiple updates to obtain common solutions of the extended exponentially general regularized nonconvex variational inequality. Furthermore, we analyze the convergence of this algorithm under various suitable conditions.

Stampacchia G, 1964, Formes Bilineaires Coercitives sur les Ensembles Convexes. Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences, 258(18): 4413.

Barbu V, 1984, Optimal Control of Variational Inequalities. Research Notes in Math, 1984(100).

Ansari Q, Lalitha C, Mehta M, 2013, Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization, CRC Press.

Daniele P, Giannessi F, Maugeri A, 2003, Equilibrium Problems and Variational Models, Dordrecht: Kluwer Academic Publishers.

Karamardian S, 1971, Generalized Complementarity Problem. Journal of Optimization Theory and Applications, 8(3): 161–168.

Clarke F, 1975, Generalized Gradients and Applications. Transactions of the American Mathematical Society, 1975(205): 247–262.

Clarke F, 1983, Nonsmooth Analysis and Optimization, Proceedings of the International Congress of Mathematicians, 1983(5): 847–853.

Clarke F, Ledyaev Y, Stern R, et al., 1998, Nonsmooth Analysis and Control Theory, Springer New York.

Poliquin R, Rockafellar R, 1996, Generalized Hessian Properties of Regularized Nonsmooth Functions. SIAM Journal on Optimization, 6(4): 1121–1137.

Poliquin R, Rockafellar R, 1996, Prox-Regular Functions in Variational Analysis. Transactions of the American Mathematical Society, 348(5): 1805–1838.

Poliquin R, Rockafellar R, Thibault L, 2000, Local Differentiability of Distance Functions. Transactions of the American Mathematical Society, 352(11): 5231–5249.

Liu L, 1995, Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces. Journal of Mathematical Analysis and Applications, 194(1): 114–125.