Discontinuous piecewise differentiable optimization I : theory

A theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems. A penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions. Although the theory is expounded in detail in the special case of discontinuous piecewise linear functions, it is straightforwardly extendable, using standard non linear programming techniques, to the nonlinear (discontinuous piecewise differentiable) situation to yield a first order algorithm. This work is presented in two parts. We introduce the theory in this first paper. The descent algorithm which is elaborated uses active set and projected gradient approaches. It is generalization of the ideas used by Conn to deal with nonsmoothness in the l1 exact penalty function, and it is based on the notion of decomposition of a function into a smooth and a nonsmooth part. In an accompanying paper, we shall tackle constraints via a penalty approach, we shall discuss the degenerate situation, the implementation of the algorithm, and numerical results will be presented

Physical Activity in Rural African School-Aged Children and Adolescents

In industrialized countries, reduced levels of physical activity (PA) associated with increased prevalence of the so-called “hypokinetic diseases” stimulates the interest in research in PA and its correlate

Níveis e padrões de actividade física de crianças e jovens de Calanga: da simples descrição à sua relevância em termos funcionais

A actividade física habitual (AF) é um comportamento associado ao estado de saúde dos sujeitos de qualquer idade. Os níveis de AF das populações de países africanos num estado de transição económica são pouco conhecidos. O propósito central deste capítulo foi o estudar de níveis de AF de crianças e adolescentes de uma comunidade rural de Moçambique (Calanga). A AF física foi avaliada recorrendo ao monitor de AF Actigraph modelo 7164 e a um questionário com questões acerca do modo e frequência de AF