Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Acetyl-L-Carnitine Prevents Methamphetamine-Induced Structural Damage on Endothelial Cells via ILK-Related MMP-9 Activity

Methamphetamine (METH) is a potent psychostimulant highly used worldwide. Recent studies evidenced the involvement of METH in the breakdown of the blood-brain-barrier (BBB) integrity leading to compromised function. The involvement of the matrix metalloproteinases (MMPs) in the degradation of the neurovascular matrix components and tight junctions (TJs) is one of the most recent findings in METH-induced toxicity. As BBB dysfunction is a pathological feature of many neurological conditions, unveiling new protective agents in this field is of major relevance. AcetylL-carnitine (ALC) has been described to protect the BBB function in different paradigms, but the mechanisms underling its action remain mostly unknown. Here, the immortalized bEnd.3 cell line was used to evaluate the neuroprotective features of ALC in METH-induced damage. Cells were exposed to ranging concentrations of METH, and the protective effect of ALC 1 mM was assessed 24 h after treatment. F-actin rearrangement, TJ expression and distribution, and MMPs activity were evaluated. Integrin-linked kinase (ILK) knockdown cells were used to assess role of ALC in ILK mediated METHtriggered MMPs’ activity. Our results show that METH led to disruption of the actin filaments concomitant with claudin-5 translocation to the cytoplasm. These events were mediated by MMP-9 activation in association with ILK overexpression. Pretreatment with ALC prevented METH-induced activation of MMP-9, preserving claudin-5 location and the structural arrangement of the actin filaments. The present results support the potential of ALC in preserving BBB integrity, highlighting ILK as a new target for the ALC therapeutic use.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.