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.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. 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: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

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.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Improvement of a filters method in a derivative free optimization

Constraints nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving the problems without constraints obtained from the original problem, have shown to be e ective, particularly when used with direct search methods. An alternative to solve the previous problems is the lters method. The lters method introduced by Fletcher and Ley er in 2002, , has been widely used to solve problems of the type mentioned above. These methods use a strategy di erent from the barrier or penalty functions. The previous functions de ne a new one that combine the objective function and the constraints, while the lters method treat optimization problems as a bi-objective problems that minimize the objective function and a function that aggregates the constraints. Motivated by the work of Audet and Dennis in 2004, using lters method with derivative-free algorithms, the authors developed works where other direct search meth- ods were used, combining their potential with the lters method. More recently. In a new variant of these methods was presented, where it some alternative aggregation restrictions for the construction of lters were proposed. This paper presents a variant of the lters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are interlinked and not treated completely independently.

Mitochondria are the main source and one of the targets of Pb (lead)-induced oxidative stress in the yeast Saccharomyces cerevisiae

The yeast Saccharomyces cerevisiae is a useful model organism for studying lead (Pb) toxicity. Yeast cells of a laboratory S. cerevisiae strain (WT strain) were incubated with Pb concentrations up to 1,000 μmol/l for 3 h. Cells exposed to Pb lost proliferation capacity without damage to the cell membrane, and they accumulated intracellular superoxide anion (O2 .−) and hydrogen peroxide (H2O2). The involvement of the mitochondrial electron transport chain (ETC) in the generation of reactive oxygen species (ROS) induced by Pb was evaluated. For this purpose, an isogenic derivative ρ0 strain, lacking mitochondrial DNA, was used. The ρ0 strain, without respiratory competence, displayed a lower intracellular ROS accumulation and a higher resistance to Pb compared to the WT strain. The kinetic study of ROS generation in yeast cells exposed to Pb showed that the production of O2 .− precedes the accumulation of H2O2, which is compatible with the leakage of electrons from the mitochondrial ETC. Yeast cells exposed to Pb displayed mutations at the mitochondrial DNA level. This is most likely a consequence of oxidative stress. In conclusion, mitochondria are an important source of Pb-induced ROS and, simultaneously, one of the targets of its toxicity.

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.

One-step preparation of optically transparent Ni-Fe oxide film electrocatalyst for oxygen evolution reaction

Optically transparent cocatalyst film materials is very desirable for improved photoelectrochemical (PEC)oxygen evolution reaction (OER) over light harvesting photoelectrodes which require the exciting light to irradiate through the cocatalyst side, i.e., front-side illumination. In view of the reaction overpotential at electrode/electrolyte interface, the OER electrocatalysts have been extensively used as cocatalysts for PEC water oxidation on photoanode. In this work, the feasibility of a one-step fabrication of the transparent thin film catalyst for efficient electrochemical OER is investigated. The Ni-Fe bimetal oxide films, 200 nm in thickness, are used for study. Using a reactive magnetron co-sputtering technique, transparent(> 50% in wavelength range 500-2000 nm) Ni-Fe oxide films with high electrocatalytic activities were successfully prepared at room temperature. Upon optimization, the as-prepared bimetal oxide film with atomic ratio of Fe/Ni = 3:7 demonstrates the lowest overpotential for the OER in aqueous KOH solution, as low as 329 mV at current density of 2 mA cm 2, which is 135 and 108 mV lower than that of as-sputtered FeOx and NiOx thin films, respectively. It appears that this fabrication strategy is very promising to deposit optically transparent cocatalyst films on photoabsorbers for efficient PEC water splitting.

RuSe Electrocatalysts and Single Wall Carbon Nanohorns Supports for the Oxygen Reduction Reaction

Selenium modified ruthenium electrocatalysts supported on carbon black were synthesized using NaBH4 reduction of the metal precursor. Prepared Ru/C electrocatalysts showed high dispersion and very small averaged particle size. These Ru/C electrocatalysts were subsequently modified with Se following two procedures: (a) preformed Ru/carbon catalyst was mixed with SeO2 in xylene and reduced in H2 and (b) Ru metal precursor was mixed with SeO2 followed by reduction with NaBH4. The XRD patterns indicate that a pyrite-type structure was obtained at higher annealing temperatures, regardless of the Ru:Se molar ratio used in the preparation step. A pyrite-type structure also emerged in samples that were not calcined; however, in this case, the pyrite-type structure was only prominent for samples with higher Ru:Se ratios. The characterization of the RuSe/C electrocatalysts suggested that the Se in noncalcined samples was present mainly as an amorphous skin. Preliminary study of activity toward oxygen reduction reaction (ORR) using electrocatalysts with a Ru:Se ratio of 1:0.7 indicated that annealing after modification with Se had a detrimental effect on their activity. This result could be related to the increased particle size of crystalline RuSe2 in heat-treated samples. Higher activity of not annealed RuSe/C catalysts could also be a result of the structure containing amorphous Se skin on the Ru crystal. The electrode obtained using not calcined RuSe showed a very promising performance with a slightly lower activity and higher overpotential in comparison with a commercial Pt/C electrode. Single wall carbon nanohorns (SWNH) were considered for application as ORR electrocatalysts' supports. The characterization of SWNH was carried out regarding their tolerance toward strong catalyzed corrosion conditions. Tests indicated that SWNH have a three times higher electrochemical surface area (ESA) loss than carbon black or Pt commercial electrodes.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

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?