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.

Electrochemical evaluation of total antioxidant capacity of beverages using a purine-biosensor

In this paper, it was evaluated the total antioxidant capacity (TAC) of beverages using an electrochemical biosensor. The biosensor consisted on the purine base (guanine or adenine) electro-immobilization on a glassy carbon electrode surface (GCE). Purine base damage was induced by the hydroxyl radical generated by Fenton-type reaction. Five antioxidants were applied to counteract the deleterious effects of the hydroxyl radical. The antioxidants used were ascorbic acid, gallic acid, caffeic acid, coumaric acid and resveratrol. These antioxidants have the ability to scavenger the hydroxyl radical and protect the guanine and adenine immobilized on the GCE surface. The interaction carried out between the purinebase immobilized and the free radical in the absence and presence of antioxidants was evaluated by means of changes in the guanine and adenine anodic peak obtained by square wave voltammetry (SWV). The results demonstrated that the purine-biosensors are suitable for rapid assessment of TAC in beverages.

Electrocatalytic evaluation of DNA damage by superoxide radical for antioxidant capacity assessment

The integrity of DNA purine bases was herein used to evaluate the antioxidant capacity. Unlike other DNA-based antioxidant sensors reported so far, the damaging agent chosen was the O 2 radical enzymatically generated by the xanthine/xanthine oxidase system. An adenine-rich oligonucleotide was adsorbed on carbon paste electrodes and subjected to radical damage in the presence/absence of several antioxidant compounds. As a result, partial damage on DNA was observed. A minor product of the radical oxidation was identified by cyclic voltammetry as a diimine adenine derivative also formed during the electrochemical oxidation of adenine/guanine bases. The protective efficiency of several antioxidant compounds was evaluated after electrochemical oxidation of the remaining unoxidized adenine bases, by measuring the electrocatalytic current of NADH mediated by the adsorbed catalyst species generated. A comparison between O 2 and OH radicals as a source of DNA lesions and the scavenging efficiency of various antioxidant compounds against both of them is discussed. Finally, the antioxidant capacity of beverages was evaluated and compared with the results obtained with an optical method.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?