Well-posedness for generalized (η,g,φ) $(\eta ,g,\varphi )$-mixed vector variational-type inequality and optimization problems

Abstract

Abstract The purpose of this paper is to focus on the well-posedness for a generalized (η,g,φ) $(\eta ,g,\varphi )$-mixed vector variational-type inequality and optimization problems with a constraint. We establish a metric characterization of well-posedness in terms of an approximate solution set. Also we prove that well-posedness of optimization problem is closely related to that of generalized (η,g,φ) $(\eta ,g,\varphi )$-mixed vector variational-type inequality problems.

Keywords

• Generalized ( η , g , φ ) $(\eta ,g,\varphi )$ -mixed vector variational-type inequality problems
• Optimization problems
• Well-posedness
• Relaxed η- α g $\alpha _{g}$ -P-monotonicity