A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Análise não suave e aplicações em otimização

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise não-diferenciável e condições necessárias de otimalidade para problema de controle ótimo com restrições mistas

Pós-graduação em Matemática - IBILCE

Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.

Birth of limit cycles bifurcating from a nonsmooth center

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)