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In this article, based on Marino and Xu's method, an iterative method which combines the regularized gradient-projection algorithm (RGPA) and the averaged mappings approach is proposed for finding a common solution of equilibrium and constrained convex minimization problems. Under suitable conditions, it is proved that the sequences generated by implicit and explicit schemes converge strongly. The results of this paper extend and improve some existing results. MSC: 58E35, 47H09, 65J15. © 2013 Tian and Huang; licensee Springer.

Regularized gradient-projection methods for equilibrium and constrained convex minimization problems