A new shrinking gradient-like projection method for equilibrium problems. (2nd December 2017)

• Record Type: Journal Article
• Authors: Hieu, Dang Van
• Is Part Of: Optimization. Volume 66:Number 12(2017)
• Page Start: 2291
• Page End: 2307
• Publication Date: 2017-12-02
• Subjects: Equilibrium problem -- variational inequality -- gradient method -- extragradient method -- hybrid method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1372437
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The paper proposes a new shrinking gradient-like projection method for solving equilibrium problems. The algorithm combines the generalized gradient-like projection method with the monotone hybrid method. Only one optimization program is solved onto the feasible set at each iteration in our algorithm without any extra-step dealing with the feasible set. The absence of an optimization problem in the algorithm is explained by constructing slightly different cutting-halfspace in the monotone hybrid method. Theorem of strong convergence is established under standard assumptions imposed on equilibrium bifunctions. An application of the proposed algorithm to multivalued variational inequality problems (MVIP) is presented. Finally, another algorithm is introduced for MVIPs in which we only use a value of main operator at the current approximation to construct the next approximation. Some preliminary numerical experiments are implemented to illustrate the convergence and computational performance of our algorithms over others.