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2014 Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems
Lu-Chuan Ceng, Cheng-Wen Liao, Chin-Tzong Pang, Ching-Feng Wen
Abstr. Appl. Anal. 2014(SI60): 1-19 (2014). DOI: 10.1155/2014/264965


We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.


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Lu-Chuan Ceng. Cheng-Wen Liao. Chin-Tzong Pang. Ching-Feng Wen. "Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems." Abstr. Appl. Anal. 2014 (SI60) 1 - 19, 2014.


Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022048
MathSciNet: MR3259155
Digital Object Identifier: 10.1155/2014/264965

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI60 • 2014
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