Dovzhenko A. Г-convergence of vector-valued mappings and their lower semicontinuous regularization

Such notions like lower semicontinuity of functional, lower semicontinuous regularization of functional and Г-convergence play great role in scalar optimization theory. The thesis is dedicated to spreading of these notions on case of vector-valued mappings, which go to semiordered by cone vector space. Two new methods of lower semicontinuous regularization of vector-valued mappings applying such constructions like epigraph and coepigraph have been built. The notion of Г-convergence has been generalized on case of vector-valued mappings. A number of important properties of such convergenct has been retrieved. Relationship between Г-convergence and Kuratowski convergence of epigraphs and coepigraphs has been shown. The theorem about compactness of Г-convergence has been proved.