A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization

This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end

A diagnostic study of temperature controls on global terrestrial carbon exchange

The observed interannual variability of atmospheric CO2 reflects short-term variability in sources and sinks of CO2 . Analyses using 13CO2 and O2 suggest that much of the observed interannual variability is due to changes in terrestrial CO2 exchange. First principles, empirical correlations and process models suggest a link between climate variation and net ecosystem exchange, but the scaling of ecological process studies to the globe is notoriously difficult. We sought to identify a component of global CO2 exchange that varied coherently with land temperature anomalies using an inverse modeling approach. We developed a family of simplified spatially aggregated ecosystem models (designated K-model versions) consisting of five compartments: atmospheric CO2 , live vegetation, litter, and two soil pools that differ in turnover times. The pools represent cumulative differences from mean C storage due to temperature variability and can thus have positive or negative values. Uptake and respiration of CO2 are assumed to be linearly dependent on temperature. One model version includes a simple representation of the nitrogen cycle in which changes in the litter and soil carbon pools result in stoichiometric release of plant-available nitrogen, the other omits the nitrogen feedback. The model parameters were estimated by inversion of the model against global temperature and CO2 anomaly data using the variational method. We found that the temperature sensitivity of carbon uptake (NPP) was less than that of respiration in all model versions. Analyses of model and data also showed that temperature anomalies trigger ecosystem changes on multiple, lagged time-scales. Other recent studies have suggested a more active land biosphere at Northern latitudes in response to warming and longer growing seasons. Our results indicate that warming should increase NPP, consistent with this theory, but that respiration should increase more than NPP, leading to decreased or negative NEP. A warming trend could, therefore increase NEP if the indirect feedbacks through nutrients were larger than the direct effects of temperature on NPP and respiration, a conjecture which can be tested experimentally. The fraction of the growth rate not predicted by the K-model represents model and data errors, and variability in anthropogenic release, ocean uptake, and other processes not explicitly represented in the model. These large positive and negative residuals from the K-model may be associated with the Southern Oscillation Index

Constrained Optimization Involving Expensive Function Evaluations:A Sequential Approach

This paper presents a new sequential method for constrained non-linear optimization problems.The principal characteristics of these problems are very time consuming function evaluations and the absence of derivative information. Such problems are common in design optimization, where time consuming function evaluations are carried out by simulation tools (e.g., FEM, CFD).Classical optimization methods, based on derivatives, are not applicable because often derivative information is not available and is too expensive to approximate through finite differencing.The algorithm first creates an experimental design. In the design points the underlying functions are evaluated.Local linear approximations of the real model are obtained with help of weighted regression techniques.The approximating model is then optimized within a trust region to find the best feasible objective improving point.This trust region moves along the most promising direction, which is determined on the basis of the evaluated objective values and constraint violations combined in a filter criterion.If the geometry of the points that determine the local approximations becomes bad, i.e. the points are located in such a way that they result in a bad approximation of the actual model, then we evaluate a geometry improving instead of an objective improving point.In each iteration a new local linear approximation is built, and either a new point is evaluated (objective or geometry improving) or the trust region is decreased.Convergence of the algorithm is guided by the size of this trust region.The focus of the approach is on getting good solutions with a limited number of function evaluations (not necessarily on reaching high accuracy).

Optimal design of phononic media through genetic algorithm-informed pre-stress for the control of antiplane wave propagation

In this paper we employ genetic algorithms in order to theoretically design a range of phononic media that can act to prevent or ensure antiplane elastic wave propagation over a specific range of low frequencies, with each case corresponding to a specific pre-stress level. The medium described consists of an array of cylindrical annuli embedded inside an elastic matrix. The annuli are considered as capable of large strain and their constitutive response is described by the popular Mooney–Rivlin strain energy function. The simple nature of the medium described is an alternative approach to topology optimization in phononic media, which although useful, often gives rise to complex phase distributions inside a composite material, leading to more complicated manufacturing requirements

Measuring atmospheric scattering from digital images of urban scenery using temporal polarization-based vision

Suspended atmospheric particles (particulate matter) are a form of air pollution that visually degrades urban scenery and is hazardous to human health and the environment. Current environmental monitoring devices are limited in their capability of measuring average particulate matter (PM) over large areas. Quantifying the visual effects of haze in digital images of urban scenery and correlating these effects to PM levels is a vital step in more practically monitoring our environment. Current image haze extraction algorithms remove all the haze from the scene and hence produce unnatural scenes for the sole purpose of enhancing vision. We present two algorithms which bridge the gap between image haze extraction and environmental monitoring. We provide a means of measuring atmospheric scattering from images of urban scenery by incorporating temporal knowledge. In doing so, we also present a method of recovering an accurate depthmap of the scene and recovering the scene without the visual effects of haze. We compare our algorithm to three known haze removal methods from the perspective of measuring atmospheric scattering, measuring depth and dehazing. The algorithms are composed of an optimization over a model of haze formation in images and an optimization using the constraint of constant depth over a sequence of images taken over time. These algorithms not only measure atmospheric scattering, but also recover a more accurate depthmap and dehazed image. The measurements of atmospheric scattering this research produces, can be directly correlated to PM levels and therefore pave the way to monitoring the health of the environment by visual means. Accurate atmospheric sensing from digital images is a challenging and under-researched problem. This work provides an important step towards a more practical and accurate visual means of measuring PM from digital images

A study of optimization and optimal control computation : exact penalty function approach

In this thesis, We propose new computational algorithms and methods for solving four classes of constrained optimization and optimal control problems. In Chapter 1, we present a brief review on optimization and optimal control. In Chapter 2, we consider a class of continuous inequality constrained optimization problems. The continuous inequality constraints are first approximated by smooth function in integral form. Then, we construct a new exact penalty function, where the summation of all these approximate smooth functions in integral form, called the constraint violation, is appended to the objective function. In this way, we obtain a sequence of approximate unconstrained optimization problems. It is shown that if the value of the penalty parameter is sufficiently large, then any local minimizer of the corresponding unconstrained optimization problem is a local minimizer of the original problem. For illustration, three examples are solved using the proposed method.From the solutions obtained, we observe that the values of their objective functions are amongst the smallest when compared with those obtained by other existing methods available in the literature. More importantly, our method finds solutions which satisfy the continuous inequality constraints.In Chapter 3, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. However, the existing gradient-based optimization techniques have difficulty to solve this equivalent nonlinear optimization problem effectively due to the new quadratic inequality constraint. Thus, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton types of methods.It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.In Chapter 4, we investigate the optimal design of allpass variable fractional delay (VFD) filters with coefficients expressed as sums of signed powers-of-two terms, where the weighted integral squared error is minimized. A new optimization procedure is proposed to generate a reduced discrete search region. Then, a new exact penalty function method is developed to solve the optimal design of allpass variable fractional delay filter with signed powers-of-two coefficients. Design examples show that the proposed method is highly effective. Compared with the conventional quantization method, the solutions obtained by our method are of much higher accuracy. Furthermore, the computational complexity is low.In Chapter 5, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent optimal control problem subject to original constraints and additional linear and quadratic constraints, where the decision variables are taking values from a feasible region, which is the union of some continuous sets. However, due to the new quadratic constraints, standard optimization techniques do not perform well when they are applied to solve the transformed problem directly.We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective function, forming a penalized objective function. This leads to a sequence of approximate optimal control problems, each of which can be solved by using optimal control techniques, and consequently, many optimal control software packages, such as MISER 3.4, can be used. Convergence results how that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude this chapter with some numerical results for two train control problems.In Chapter 6, some concluding remarks and suggestions for future research directions are made

Nature’s Optics and Our Understanding of Light

Optical phenomena visible to everyone abundantly illustrate important ideas in science and mathematics. The phenomena considered include rainbows, sparkling reflections on water, green flashes, earthlight on the moon, glories, daylight, crystals, and the squint moon. The concepts include refraction, wave interference, numerical experiments, asymptotics, Regge poles, polarisation singularities, conical intersections, and visual illusions

Performance limits in optical communications due to fiber nonlinearity

In this paper, we review the historical evolution of predictions of the performance of optical communication systems. We will describe how such predictions were made from the outset of research in laser based optical communications and how they have evolved to their present form, accurately predicting the performance of coherently detected communication systems

Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws

A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities and vortex flows. Overall, it is shown that the proposed hybrid method results in comparable or better simulation results compared with the standalone WENO scheme when the same number of solution DOF is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the Journal of Computational Physics, April 201