TAILIEUCHUNG - An iteration method for a convex optimization over the fixed point set of a nonexpansive mapping

In this paper, we introduce a new iteration method, that is a combination of the hybrid steepestdescent method with two-step iteration method of linearization, for finding a minimizer of a convex differentiable functional over the fixed point set of a nonexpansive mapping in Hilbert spaces. Key words: Metric projection, Fixed point, Nonexpansive Mappings. | Nguyễn Bường và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 99(11): 161 - 164 AN ITERATION METHOD FOR A CONVEX OPTIMIZATION OVER THE FIXED POINT SET OF A NONEXPANSIVE MAPPING Nguyen Buong1*, Nguyen Duong Nguyen2 1 Vietnamese Academy of Science and Technology 2 Vietnam Foreign Trade University SUMMARY In this paper, we introduce a new iteration method, that is a combination of the hybrid steepestdescent method with two-step iteration method of linearization, for finding a minimizer of a convex differentiable functional over the fixed point set of a nonexpansive mapping in Hilbert spaces. Key words: Metric projection, Fixed point, Nonexpansive Mappings. AMS 2000 Mathematics Subject Classification (MSC): 41A65, 47H17, 47H20. INTRODUCTION* Let H be a real Hilbert space with the scalar product and norm denoted by the symbols and

• Toán học
• An iteration method for a convex optimization over
• The fixed point set
• A nonexpansive mapping
• Mathematics Subject Classification
• Two step iteration method