Optimal Control of Nonconvex Differential Inclusions

The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper

Variational Analysis of Evolution Inclusions

The paper is devoted to optimization problems of the Bolza and Mayer types for evolution systems governed by nonconvex Lipschitzian differential inclusions in Banach spaces under endpoint constraints described by finitely many equalities and inequalities. with generally nonsmooth functions. We develop a variational analysis of such roblems mainly based on their discrete approximations and the usage of advanced tools of generalized differentiation satisfying comprehensive calculus rules in the framework of Asplund (and hence any reflexive Banach) spaces. In this way we establish extended results on stability of discrete approximations (with the strong W^1,2-convergence of optimal solutions under consistent perturbations of endpoint constraints) and derive necessary optimality conditions for nonconvex discrete-time and continuous-time systems in the refined Euler-Lagrange and Weierstrass-Pontryagin forms accompanied by the appropriate transversality inclusions. In contrast to the case of geometric endpoint constraints in infinite dimensions, the necessary optimality conditions obtained in this paper do not impose any nonempty interiority /finite codimension/normal compactness assumptions. The approach and results developed in the paper make a bridge between optimal control/dynamic optimization and constrained mathematical programming problems in infinite-dimensional spaces

Error bounds and metric subregularity

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes

Subdifferentials of distance functions in Banach spaces.

Ng, Kwong Wing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (p. 123-126).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiContents --- p.vIntroduction --- p.viiChapter 1 --- Preliminaries --- p.1Chapter 1.1 --- Basic Notations and Conventions --- p.1Chapter 1.2 --- Fundamental Results in Banach Space Theory and Variational Analysis --- p.4Chapter 1.3 --- Set-Valued Mappings --- p.6Chapter 1.4 --- Enlargements and Projections --- p.8Chapter 1.5 --- Subdifferentials --- p.11Chapter 1.6 --- Sets of Normals --- p.18Chapter 1.7 --- Coderivatives --- p.24Chapter 2 --- The Generalized Distance Function - Basic Estimates --- p.27Chapter 2.1 --- Elementary Properties of the Generalized Distance Function --- p.27Chapter 2.2 --- Frechet-Like Subdifferentials of the Generalized Distance Function --- p.32Chapter 2.3 --- Limiting and Singular Subdifferentials of the Generalized Distance - Function --- p.44Chapter 3 --- The Generalized Distance Function - Estimates via Intermediate Points --- p.73Chapter 3.1 --- Frechet-Like and Limiting Subdifferentials of the Generalized Dis- tance Function via Intermediate Points --- p.74Chapter 3.2 --- Frechet and Proximal Subdifferentials of the Generalized Distance Function via Intermediate Points --- p.90Chapter 4 --- The Marginal Function --- p.95Chapter 4.1 --- Singular Subdifferentials of the Marginal Function --- p.95Chapter 4.2 --- Singular Subdifferentials of the Generalized Marginal Function . . --- p.102Chapter 5 --- The Perturbed Distance Function --- p.107Chapter 5.1 --- Elementary Properties of the Perturbed Distance Function --- p.107Chapter 5.2 --- The Convex Case - Subdifferentials of the Perturbed Distance Function --- p.111Chapter 5.3 --- The Nonconvex Case - Frechet-Like and Proximal Subdifferentials of the Perturbed Distance Function --- p.113Bibliography --- p.12

Book of Abstracts

USPCAPESFAPESPCNPqINCTMatICMC Summer Meeting on Differentail Equations.\ud São Carlos, Brasil. 3-7 february 2014

Nondifferentiable Optimization: Motivations and Applications

IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984. This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications