Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Solid Lipid Nanoparticles For Hydrophilic Biotech Drugs: Optimization And Cell Viability Studies (caco-2 & Hepg-2 Cell Lines).

Insulin was used as model protein to developed innovative Solid Lipid Nanoparticles (SLNs) for the delivery of hydrophilic biotech drugs, with potential use in medicinal chemistry. SLNs were prepared by double emulsion with the purpose of promoting stability and enhancing the protein bioavailability. Softisan(®)100 was selected as solid lipid matrix. The surfactants (Tween(®)80, Span(®)80 and Lipoid(®)S75) and insulin were chosen applying a 2(2) factorial design with triplicate of central point, evaluating the influence of dependents variables as polydispersity index (PI), mean particle size (z-AVE), zeta potential (ZP) and encapsulation efficiency (EE) by factorial design using the ANOVA test. Therefore, thermodynamic stability, polymorphism and matrix crystallinity were checked by Differential Scanning Calorimetry (DSC) and Wide Angle X-ray Diffraction (WAXD), whereas the effect of toxicity of SLNs was check in HepG2 and Caco-2 cells. Results showed a mean particle size (z-AVE) width between 294.6 nm and 627.0 nm, a PI in the range of 0.425-0.750, ZP about -3 mV, and the EE between 38.39% and 81.20%. After tempering the bulk lipid (mimicking the end process of production), the lipid showed amorphous characteristics, with a melting point of ca. 30 °C. The toxicity of SLNs was evaluated in two distinct cell lines (HEPG-2 and Caco-2), showing to be dependent on the concentration of particles in HEPG-2 cells, while no toxicity in was reported in Caco-2 cells. SLNs were stable for 24 h in in vitro human serum albumin (HSA) solution. The resulting SLNs fabricated by double emulsion may provide a promising approach for administration of protein therapeutics and antigens.

Electrochemical Oxidation Of Landfill Leachate In A Flow Reactor: Optimization Using Response Surface Methodology.

Response surface methodology based on Box-Behnken (BBD) design was successfully applied to the optimization in the operating conditions of the electrochemical oxidation of sanitary landfill leachate aimed for making this method feasible for scale up. Landfill leachate was treated in continuous batch-recirculation system, where a dimensional stable anode (DSA(©)) coated with Ti/TiO2 and RuO2 film oxide were used. The effects of three variables, current density (milliampere per square centimeter), time of treatment (minutes), and supporting electrolyte dosage (moles per liter) upon the total organic carbon removal were evaluated. Optimized conditions were obtained for the highest desirability at 244.11 mA/cm(2), 41.78 min, and 0.07 mol/L of NaCl and 242.84 mA/cm(2), 37.07 min, and 0.07 mol/L of Na2SO4. Under the optimal conditions, 54.99 % of chemical oxygen demand (COD) and 71.07 ammonia nitrogen (NH3-N) removal was achieved with NaCl and 45.50 of COD and 62.13 NH3-N with Na2SO4. A new kinetic model predicted obtained from the relation between BBD and the kinetic model was suggested.

Spectral Region Optimization for Raman-Based Optical Biopsy of Inflammatory Lesions

Objective: The biochemical alterations between inflammatory fibrous hyperplasia (IFH) and normal tissues of buccal mucosa were probed by using the FT-Raman spectroscopy technique. The aim was to find the minimal set of Raman bands that would furnish the best discrimination. Background: Raman-based optical biopsy is a widely recognized potential technique for noninvasive real-time diagnosis. However, few studies had been devoted to the discrimination of very common subtle or early pathologic states as inflammatory processes that are always present on, for example, cancer lesion borders. Methods: Seventy spectra of IFH from 14 patients were compared with 30 spectra of normal tissues from six patients. The statistical analysis was performed with principal components analysis and soft independent modeling class analogy cross-validated, leave-one-out methods. Results: Bands close to 574, 1,100, 1,250 to 1,350, and 1,500 cm(-1) (mainly amino acids and collagen bands) showed the main intragroup variations that are due to the acanthosis process in the IFH epithelium. The 1,200 (C-C aromatic/DNA), 1,350 (CH(2) bending/collagen 1), and 1,730 cm(-1) (collagen III) regions presented the main intergroup variations. This finding was interpreted as originating in an extracellular matrix-degeneration process occurring in the inflammatory tissues. The statistical analysis results indicated that the best discrimination capability (sensitivity of 95% and specificity of 100%) was found by using the 530-580 cm(-1) spectral region. Conclusions: The existence of this narrow spectral window enabling normal and inflammatory diagnosis also had useful implications for an in vivo dispersive Raman setup for clinical applications.

Optimization of the Enzymatic Interesterification of Milk Fat and Canola Oil Blends Using Immobilized Rhizopus oryzae Lipase by Response Surface Methodology

Blends of milk fat and canola oil (MF:CNO) were enzymatically interesterified (EIE) by Rhizopus oryzne lipase immobilized on polysiloxane-polyvinyl alcohol (SiO(2)-PVA) composite, in a solvent-free system. A central composite design (CCD) was used to optimize the reaction, considering the effects of different mass fractions of binary blends of MF:CNO (50:50, 65:35 and 80:20) and temperatures (45, 55 and 65 degrees C) on the composition and texture properties of the interesterified products, taking the interesterification degree (ID) and consistency (at 10 degrees C) as response variables. For the ID variable both mass fraction of milk fat in the blend and temperature were found to be significant, while for the consistency only mass fraction of milk fat was significant. Empiric models for ID and consistency were obtained that allowed establishing the best interesterification conditions: blend with 65 % of milk fat and 35 %, of canola oil, and temperature of 45 degrees C. Under these conditions, the ID was 19.77 %) and the consistency at 10 degrees C was 56 290 Pa. The potential of this eco-friendly process demonstrated that a product could be obtained with the desirable milk fat flavour and better spreadability under refrigerated conditions.

Risk optimization of a steel frame communications tower subject to tornado winds

The structural engineering community in Brazil faces new challenges with the recent occurrence of high intensity tornados. Satellite surveillance data shows that the area covering the south-east of Brazil, Uruguay and some of Argentina is one of the world most tornado-prone areas, second only to the infamous tornado alley in central United States. The design of structures subject to tornado winds is a typical example of decision making in the presence of uncertainty. Structural design involves finding a good balance between the competing goals of safety and economy. This paper presents a methodology to find the optimum balance between these goals in the presence of uncertainty. In this paper, reliability-based risk optimization is used to find the optimal safety coefficient that minimizes the total expected cost of a steel frame communications tower, subject to extreme storm and tornado wind loads. The technique is not new, but it is applied to a practical problem of increasing interest to Brazilian structural engineers. The problem is formulated in the partial safety factor format used in current design codes, with all additional partial factor introduced to serve as optimization variable. The expected cost of failure (or risk) is defined as the product of a. limit state exceedance probability by a limit state exceedance cost. These costs include costs of repairing, rebuilding, and paying compensation for injury and loss of life. The total expected failure cost is the sum of individual expected costs over all failure modes. The steel frame communications, tower subject of this study has become very common in Brazil due to increasing mobile phone coverage. The study shows that optimum reliability is strongly dependent on the cost (or consequences) of failure. Since failure consequences depend oil actual tower location, it turn,,; out that different optimum designs should be used in different locations. Failure consequences are also different for the different parties involved in the design, construction and operation of the tower. Hence, it is important that risk is well understood by the parties involved, so that proper contracts call be made. The investigation shows that when non-structural terms dominate design costs (e.g, in residential or office buildings) it is not too costly to over-design; this observation is in agreement with the observed practice for non-optimized structural systems. In this situation, is much easier to loose money by under-design. When by under-design. When structural material cost is a significant part of design cost (e.g. concrete dam or bridge), one is likely to lose significantmoney by over-design. In this situation, a cost-risk-benefit optimization analysis is highly recommended. Finally, the study also shows that under time-varying loads like tornados, the optimum reliability is strongly dependent on the selected design life.

Multidisciplinary optimization of a catamaran's hydrofoil design with dynamic response surface and distributive processing

This paper presents a rational approach to the design of a catamaran's hydrofoil applied within a modern context of multidisciplinary optimization. The approach used includes the use of response surfaces represented by neural networks and a distributed programming environment that increases the optimization speed. A rational approach to the problem simplifies the complex optimization model; when combined with the distributed dynamic training used for the response surfaces, this model increases the efficiency of the process. The results achieved using this approach have justified this publication.

Social interaction as a heuristic for combinatorial optimization problems

We investigate the performance of a variant of Axelrod's model for dissemination of culture-the Adaptive Culture Heuristic (ACH)-on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(1/4) so that the number of agents must increase with the fourth power of the problem size, N proportional to F(4), to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F(6) which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success.

Estimation of the thickness and the optical parameters of several stacked thin films using optimization

The reverse engineering problem addressed in the present research consists of estimating the thicknesses and the optical constants of two thin films deposited on a transparent substrate using only transmittance data through the whole stack. No functional dispersion relation assumptions are made on the complex refractive index. Instead, minimal physical constraints are employed, as in previous works of some of the authors where only one film was considered in the retrieval algorithm. To our knowledge this is the first report on the retrieval of the optical constants and the thickness of multiple film structures using only transmittance data that does not make use of dispersion relations. The same methodology may be used if the available data correspond to normal reflectance. The software used in this work is freely available through the PUMA Project web page (http://www.ime.usp.br/similar to egbirgin/puma/). (C) 2008 Optical Society of America

Simultaneous optimization by neuro-genetic approach for analysis of plant materials by laser induced breakdown spectroscopy

A simultaneous optimization strategy based on a neuro-genetic approach is proposed for selection of laser induced breakdown spectroscopy operational conditions for the simultaneous determination of macronutrients (Ca, Mg and P), micro-nutrients (B, Cu, Fe, Mn and Zn), Al and Si in plant samples. A laser induced breakdown spectroscopy system equipped with a 10 Hz Q-switched Nd:YAG laser (12 ns, 532 nm, 140 mJ) and an Echelle spectrometer with intensified coupled-charge device was used. Integration time gate, delay time, amplification gain and number of pulses were optimized. Pellets of spinach leaves (NIST 1570a) were employed as laboratory samples. In order to find a model that could correlate laser induced breakdown spectroscopy operational conditions with compromised high peak areas of all elements simultaneously, a Bayesian Regularized Artificial Neural Network approach was employed. Subsequently, a genetic algorithm was applied to find optimal conditions for the neural network model, in an approach called neuro-genetic, A single laser induced breakdown spectroscopy working condition that maximizes peak areas of all elements simultaneously, was obtained with the following optimized parameters: 9.0 mu s integration time gate, 1.1 mu s delay time, 225 (a.u.) amplification gain and 30 accumulated laser pulses. The proposed approach is a useful and a suitable tool for the optimization process of such a complex analytical problem. (C) 2009 Elsevier B.V. All rights reserved.

Optimization and validation of a LIBS method for the determination of macro and micronutrients in sugar cane leaves

Laser induced breakdown spectrometry (LIBS) was applied for the determination of macro (P, K, Ca, Mg) and micronutrients (B, Cu, Fe, Mn and Zn) in sugar cane leaves, which is one of the most economically important crops in Brazil. Operational conditions were previously optimized by a neuro-genetic approach, by using a laser Nd:YAG at 1064 nm with 110 mJ per pulse focused on a pellet surface prepared with ground plant samples. Emission intensities were measured after 2.0 mu s delay time, with 4.5 mu s integration time gate and 25 accumulated laser pulses. Measurements of LIBS spectra were based on triplicate and each replicate consisted of an average of ten spectra collected in different sites (craters) of the pellet. Quantitative determinations were carried out by using univariate calibration and chemometric methods, such as PLSR and iPLS. The calibration models were obtained by using 26 laboratory samples and the validation was carried out by using 15 test samples. For comparative purpose, these samples were also microwave-assisted digested and further analyzed by ICP OES. In general, most results obtained by LIBS did not differ significantly from ICP OES data by applying a t-test at 95% confidence level. Both LIBS multivariate and univariate calibration methods produced similar results, except for Fe where better results were achieved by the multivariate approach. Repeatability precision varied from 0.7 to 15% and 1.3 to 20% from measurements obtained by multivariate and univariate calibration, respectively. It is demonstrated that LIBS is a powerful tool for analysis of pellets of plant materials for determination of macro and micronutrients by choosing calibration and validation samples with similar matrix composition.

Exercise intensity optimization for men with high cardiorespiratory fitness

Exercise intensity is a key parameter for exercise prescription but the optimal range for individuals with high cardiorespiratory fitness is unknown. The aims of this study were (1) to determine optimal heart rate ranges for men with high cardiorespiratory fitness based on percentages of maximal oxygen consumption (%VO(2max)) and reserve oxygen consumption (%VO(2reserve)) corresponding to the ventilatory threshold and respiratory compensation point, and ( 2) to verify the effect of advancing age on the exercise intensities. Maximal cardiorespiratory testing was performed on 210 trained men. Linear regression equations were calculated using paired data points between percentage of maximal heart rate (%HR(max)) and %VO(2max) and between percentage of heart rate reserve (%HRR) and %VO(2reserve) attained at each minute during the test. Values of %VO(2max) and %VO(2reserve) at the ventilatory threshold and respiratory compensation point were used to calculate the corresponding values of %HRmax and %HRR, respectively. The ranges of exercise intensity in relation to the ventilatory threshold and respiratory compensation point were achieved at 78-93% of HR(max) and 70-93% of HRR, respectively. Although absolute heart rate decreased with advancing age, there were no age-related differences in %HR(max) and %HRR at the ventilatory thresholds. Thus, in men with high cardiorespiratory fitness, the ranges of exercise intensity based on %HR(max) and %HRR regarding ventilatory threshold were 78-93% and 70-93% respectively, and were not influenced by advancing age.

Optimization of the AZO dyes decoloration process through neural networks: Determination of the H2O2 addition critical point

The concentration of hydrogen peroxide is an important parameter in the azo dyes decoloration process through the utilization of advanced oxidizing processes, particularly by oxidizing via UV/H2O2. It is pointed out that, from a specific concentration, the hydrogen peroxide works as a hydroxyl radical self-consumer and thus a decrease of the system`s oxidizing power happens. The determination of the process critical point (maximum amount of hydrogen peroxide to be added) was performed through a ""thorough mapping"" or discretization of the target region, founded on the maximization of an objective function objective (constant of reaction kinetics of pseudo-first order). The discretization of the operational region occurred through a feedforward backpropagation neural model. The neural model obtained presented remarkable coefficient of correlation between real and predicted values for the absorbance variable, above 0.98. In the present work, the neural model had, as phenomenological basis the Acid Brown 75 dye decoloration process. The hydrogen peroxide addition critical point, represented by a value of mass relation (F) between the hydrogen peroxide mass and the dye mass, was established in the interval 50 < F < 60. (C) 2007 Elsevier B.V. All rights reserved.

Optimization of Heat Treatment Profiles Applied to Nanometric-Scale Nb(3)Sn Wires With Cu-Sn Artificial Pinning Centers

Nb(3)Sn is one of the most used superconducting materials for applications in high magnetic fields. The improvement of the critical current densities (J(c)) is important, and must be analyzed together with the optimization of the flux pinning acting in the material. For Nb(3)Sn, it is known that the grain boundaries are the most effective pinning centers. However, the introduction of artificial pinning centers (APCs) with different superconducting properties has been proved to be beneficial for J(c). As these APCs are normally in the nanometric-scale, the conventional heat treatment profiles used for Nb(3)Sn wires cannot be directly applied, leading to excessive grain growth and/or increase of the APCs cross sections. In this work, the heat treatment profiles for Nb(3)Sn superconductor wires with Cu(Sn) artificial pinning centers in nanometric-scale were analyzed in an attempt to improve J(c) . It is described a methodology to optimize the heat treatment profiles in respect to diffusion, reaction and formation of the superconducting phases. Microstructural, transport and magnetic characterization were performed in an attempt to find the pinning mechanisms acting in the samples. It was concluded that the maximum current densities were found when normal phases (due to the introduction of the APCs) are acting as main pinning centers in the global behavior of the Nb(3)Sn superconducting wire.

Improved xylitol production in media containing phenolic aldehydes: application of response surface methodology for optimization and modeling of bioprocess

BACKGROUND: The combined effects of vanillin and syringaldehyde on xylitol production by Candida guilliermondii using response surface methodology (RSM) have been studied. A 2(2) full-factorial central composite design was employed for experimental design and analysis of the results. RESULTS: Maximum xylitol productivities (Q(p) = 0.74 g L(-1) h(-1)) and yields (Y(P/S) = 0.81 g g(-1)) can be attained by adding only vanillin at 2.0 g L(-1) to the fermentation medium. These data were closely correlated with the experimental results obtained (0.69 +/- 0.04 g L(-1) h(-1) and 0.77 +/- 0.01 g g(-1)) indicating a good agreement with the predicted value. C. guilliermondii was able to convert vanillin completely after 24 h of fermentation with 94% yield of vanillyl alcohol. CONCLUSIONS: The bioconversion of xylose into xylitol by C. guilliermondii is strongly dependent on the combination of aldehydes and phenolics in the fermentation medium. Vanillin is a source of phenolic compound able to improve xylitol production by yeast. The conversion of vanillin to alcohol vanilyl reveals the potential of this yeast for medium detoxification. (C) 2009 Society of Chemical Industry