An algorithmic approach to prox-regular variational inequalities. (English) Zbl 1062.65071

The author introduces a prox-gradient method for solving the nonconvex variational inequality problem and shows that the prox-regularity is enough to guarantee its local linear convergence. The main result of the paper can be considered as an improvement and a significant extension of some known results. The technique of the proof of the main result is very interesting.


65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
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[1] Cottle, R.W; Giannessi, F; Lions, J.L, Variational inequalities and complementarity problems: theory and applications, (1980), John Wiley and Sons New York
[2] Giannessi, F; Maugeri, A, Variational inequalities and network equilibrium problems, (1995), Plenum Press New York · Zbl 0834.00044
[3] Bounkhel, M; Tadji, L; Hamdi, A, Iterative schemes to solve nonconvex variational problems, J. inequal. pure appl. math., 4, 1, (2003), Article 14
[4] Kaplan, A; Tichatschke, R, Proximal point methods and nonconvex optimiztion, J. global optim., 13, 389-406, (1998) · Zbl 0916.90224
[5] B. Lemaire, Quelques résultats récents sur l’algorithme proximal, Séminaire d’analyse Numérique Toulouse, 1990
[6] Pennaen, T, Local convergence of the proximal point algorithm and multiplier methods without monotonicity, Math. oper. res., 27, 170-191, (2002)
[7] Spingarn, J.E, Submonotone mappings and the proximal point algorithm, J. numer. funct. anal. optim., 4, 123-150, (1981) · Zbl 0495.49025
[8] Poliquin, R.A; Rockafellar, R.T, Prox-regular functions in variational analysis, Trans. am. math. soc., 248, 5, 1805-1838, (1996) · Zbl 0861.49015
[9] Rockafellar, R.T; Wets, R.J.-B, Variational analysis, (1998), Springer Berlin · Zbl 0888.49001
[10] Moudafi, A; Aslam Noor, M, New convergence results for iterative methods for set-valued mixed variational inequalities, J. math. inequal. appl., 3, 223-232, (2000)
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