Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

HIV Voluntary Testing among Portuguese Women Attending Family Planning Clinics: Implications for HIV Prevention Education and Testing

Objectives: The aim of this article is to analyze the factors associated with HIV testing among 767 sexually active women. Methods: Participants were administered several self-report questionnaires that assessed behavioral and psychosocial measures. Results: Overall, 59.8% of the participants reported ever having tested for HIV. Results show that higher levels of education, being pregnant or having been pregnant, concern about AIDS, AIDS knowledge, self-efficacy in condom negotiation and perception of no risk in partner significantly predicted the likelihood of testing among women. Attending the mass was negatively associated with HIV testing. Conclusions: These findings provide information that can be used in the development of a focused gender sensitive HIV prevention program to increase HIV testing.