Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators
- 39 Downloads
In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert spaces. The algorithm is designed such that the stepsizes are dynamically chosen and its convergence is guaranteed without the Lipschitz continuity and the paramonotonicity of the underlying operator. We will show that the proposed algorithm yields strong convergence without being combined with the hybrid/viscosity or linesearch methods. Our results improve and develop previously discussed gradient projection-type algorithms by Khanh and Vuong (J. Global Optim. 58, 341–350 2014).
KeywordsVariational inequality Monotone operator Gradient projection algorithm Extragradient algorithm Subgradient extragradient algorithm Projected reflected gradient method Inertial-type algorithm
Mathematics Subject Classification (2010)47J20 90C25
Unable to display preview. Download preview PDF.
The authors would like to thanks the editor and the referee for valuable remarks and helpful suggestions which improved the quality of the paper.
The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.08. His research is also partially supported by the Vietnam Institute for Advanced Study in Mathematics and by UTC under Grant T2019-CB-014.
- 9.Combettes, P.L.: Quasi-Fejérian analysis of some optimization algorithms. In: Butnariu, D., Censor, Y., Reich, S. (eds.) Inherently Parallel Algorithms for Feasibility and Optimization, pp 115–152. Elsevier, New York (2001)Google Scholar
- 14.Vector Variational Inequalities and Vector Equilibria: Mathematical Theories Nonconvex Optimization and Its Applications. In: Giannessi, F. (ed.) , vol. 38. Kluwer, Dordrecht (2000)Google Scholar
- 34.Tinti, F.: Numerical Solution for Pseudomonotone Variational Inequality Problems by Extragradient Methods. (English summary) Variational Analysis and Applications, 1101–1128, Nonconvex Optim Appl., 79. Springer, New York (2005)Google Scholar