Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces. (2nd June 2016)

• Record Type: Journal Article
• Authors: Cianciaruso, Filomena; Marino, Giuseppe; Muglia, Luigi; Xu, Hong-Kun
• Is Part Of: Optimization. Volume 65:Number 6(2016)
• Page Start: 1259
• Page End: 1275
• Publication Date: 2016-06-02
• Subjects: variational inequality -- -hybrid -- iterative method -- ergodic -- nonspreading mappings -- Cesaro's means -- regular matrix; 47J20 -- 47J25 -- 49J40 -- 65J15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1091824
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann's method) with regularized processes involved regular matrices in the sense of Toeplitz.