Hemivariational Inequality Approach to Evolutionary Constrained Problems on Star-Shaped Sets

作者：Gasinski, Leszek; Liu, Zhenhai; Migorski, Stanislaw; Ochal, Anna; Peng, Zijia^*

来源：Journal of Optimization Theory and Applications, 2015, 164(2): 514-533.

DOI：10.1007/s10957-014-0587-6

• Variational inequality
• Evolutionary inclusion
• Star-shaped set
• L-pseudomonotone operator
• Clarke subgradient
• Distance function
• Surjectivity result

In this paper, we consider a nonconvex evolutionary constrained problem for a star-shaped set. The problem is a generalization of the classical evolution variational inequality of parabolic type. We provide an existence result; the proof is based on the hemivariational inequality approach, a surjectivity theorem for multivalued pseudomonotone operators in reflexive Banach spaces, and a penalization method. The admissible set of constraints is closed and star-shaped with respect to a certain ball; this allows one to use a discontinuity property of the generalized Clarke subdifferential of the distance function. An application of our results to a heat conduction problem with nonconvex constraints is provided.

• 出版日期2015-2
• 单位广西民族大学