
Unilateral Variational Analysis in Banach Spaces. Part II: Special Classes of Functions and Sets
Authors: Thibault
Editor: World Scientific
Publication date: 2023
Related research areas: Functional analysis, Geometry of Banach spaces, Modern Convex Analysis, Variational Nonsmooth Analysis
The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems. The second volume is devoted to special classes of nonsmooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of nonsmooth mappings, of proxregular functions and sets in general spaces, of differentiability of projection mapping and others for proxregular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments. Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.
Summary:
Contents: Part II: Subsmooth Functions and SetsSubdifferential DeterminationSemiconvex FunctionsPrimal Lower Regular Functions and ProxRegular FunctionsSingular Points of Nonsmooth FunctionsNonDifferentiability Points of Functions on Separable Banach SpacesDistance Function, Metric Projection and Moreau EnvelopeProxRegularity of Sets In Hilbert SpaceCompatible Parametrization and Vial Property of ProxRegular Sets, Exterior Sphere ConditionDifferentiability of Metric Projection Onto ProxRegular SetsProxRegularity of Sets in Uniformly Convex Banach SpacesAppendices: TopologyTopological Properties of Convex SetsFunctional AnalysisMeasure TheoryDifferential Calculus and Differentiable Manifolds More info herecover