Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces

This paper concerns a generalized equation defined by a closed multifunction between Banach spaces, and we employ variational analysis techniques to provide sufficient and/or necessary conditions for a generalized equation to have the metric subregularity (i.e., local error bounds for the concerned multifunction) in general Banach spaces. Following the approach of Ioffe [Trans. Amer. Math. Soc., 251 (1979), pp. 61–69] who studied the numerical function case, our conditions are described in terms of coderivatives of the concerned multifunction at points outside the solution set. Motivated by the existing modulus representation and point-based criteria for the metric regularity, we establish the corresponding results for the metric subregularity. In the Asplund space case, sharper results are obtained. Key words. metric subregularity, calmness, coderivative, normal cone, normal dual mapping AMS subject classifications. 90C31, 90C25, 49J52 DOI. 10.1137/090772174

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Xi Yin Zheng, Kung Fu Ng
• Keywords: Concerned Multifunction, Generalized Equation, Metric Subregularity, SIAMJO 2010