Constrained Optimization Method Research Articles

Identification and updating for the three‐dimensional finite element model of a long span steel skybridge

AbstractAn identification and updating procedure for the three‐dimensional finite element (FE) model of a long span steel skybridge is presented in this paper. Located at an elevation of 90 m, the skybridge is one of the six skybridges of Hangzhou Citizen Center, which is a hexadic‐tower tall building. The modal data of the skybridge is first estimated using output only identification method, and sensitivity‐based updating method is then applied to update the three‐dimensional FE model based on the estimated modal data. For the modal data identification, a time domain least square method and a data smoothing method were applied for pre‐processing the recorded acceleration time histories. The averaged normalized power spectral density was then used in the peak‐picking method to identify the natural frequencies. The updating algorithm is composed of sensitivity analysis and Bayesian estimation, and the parameter perturbations are estimated using a constrained optimization method. It is found that far better matches can be reached between the updated and estimated dynamic characteristics by using the proposed identification and updating procedure. Copyright © 2009 John Wiley & Sons, Ltd.

A new technique for avoiding the Maratos effect

A well-known difficulty arising in the convergence globalization of Newton-type constrained optimization methods is the Maratos effect, which prevents these methods from achieving a superlinear convergence rate and, in many cases, reduces their general efficiency. For the sequential quadratic programming method with linesearch, a new simple and rather promising technique is proposed to avoid the Maratos effect.

A Biophysically Inspired Model for Contrast Adaptation

Event Abstract Back to Event A Biophysically Inspired Model for Contrast Adaptation Contrast adaptation is a process that changes the gain, kinetics and baseline membrane potential of retinal ganglion cells over timescales that range from less than 100 ms to tens of seconds. Several models have been proposed that can replicate some of these adaptive processes (Borst et al, 2005, Gaudry, Reinagel 2007, Mante et al, 2008), although it is not clear how these models translate into biophysical mechanisms. Here we present a simple biophysically inspired model of an adaptive cell that tracks the gain with sub-second precision and replicates fast kinetic and baseline membrane potential changes of salamander retinal ganglion cells over a wide range of contrasts. The model is comprised of three sequential stages, a linear filter, a static nonlinearity and a three state first order kinetic model. We recorded from ganglion cells intracellularly while presenting a uniform field visual stimulus. The light intensity was drawn from a Gaussian distribution every 30 ms, and every 20 s the standard deviation of the distribution changed randomly to between 10 % and 40 % of the mean intensity. The parameters of the model were fit using a constrained optimization method to minimize the error between the model and the membrane potential response. The overall correlation between the actual and estimated responses was 72% for a single set of model parameters whereas it was 65% when we used many separate Linear-Nonlinear (LN) models fit to each contrast. In the adaptive stage of the model, the states can be thought of as representing “available”, “active” and “unavailable” states of a biophysical mechanism. This flexible framework can be applied to ion channels that inactivate, synapse vesicle pools that experience depression, or neurotransmitter receptors that desensitize. With three states and one rate constant that is set by the output of the static nonlinearity, increases in contrast produce a Weber-like change in gain, an acceleration in kinetics, an increase in baseline, and asymmetric dynamics in the response, as is seen experimentally. These changes are intrinsic to the adaptive stage without the need for an additional pathway to control the response properties. The incorporation of an additional state or input-dependent rate constant produces additional, slower timescales of adaptation. Although this model is applied here to the process of contrast adaptation, the adaptive stage changes the overall response properties by virtue of a change in mean produced by the output of the threshold nonlinearity at different contrasts. As such, this type of adaptive stage may be applicable to other types of adaptation such as luminance adaptation with a different input stage. A simple biophysical model can capture multiple phenomena of adaptation, indicating that seemingly distinct adaptive processes could be generated even by a single molecule with just a few states. The parameters of this model can be to used design and interpret experiments on the mechanisms that produce these adaptive properties. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). A Biophysically Inspired Model for Contrast Adaptation. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.346 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 10 Feb 2009; Published Online: 10 Feb 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Blind Channel Equalization with Colored Source Based on Constrained Optimization Methods

Tsatsanis and Xu have applied the constrained minimum output variance (CMOV) principle to directly blind equalize a linear channel—a technique that has proven effective with white inputs. It is generally assumed in the literature that their CMOV method can also effectively equalize a linear channel with a colored source. In this paper, we prove that colored inputs will cause the equalizer to incorrectly converge due to inadequate constraints. We also introduce a new blind channel equalizer algorithm that is based on the CMOV principle, but with a different constraint that will correctly handle colored sources. Our proposed algorithm works for channels with either white or colored inputs and performs equivalently to the trained minimum mean-square error (MMSE) equalizer under high SNR. Thus, our proposed algorithm may be regarded as an extension of the CMOV algorithm proposed by Tsatsanis and Xu. We also introduce several methods to improve the performance of our introduced algorithm in the low SNR condition. Simulation results show the superior performance of our proposed methods.

A Constrained Line Search Optimization Method for Discriminative Training of HMMs

In this paper, we propose a novel optimization algorithm called constrained line search (CLS) for discriminative training (DT) of Gaussian mixture continuous density hidden Markov model (CDHMM) in speech recognition. The CLS method is formulated under a general framework for optimizing any discriminative objective functions including maximum mutual information (MMI), minimum classification error (MCE), minimum phone error (MPE)/minimum word error (MWE), etc. In this method, discriminative training of HMM is first cast as a constrained optimization problem, where Kullback-Leibler divergence (KLD) between models is explicitly imposed as a constraint during optimization. Based upon the idea of line search, we show that a simple formula of HMM parameters can be found by constraining the KLD between HMM of two successive iterations in an quadratic form. The proposed CLS method can be applied to optimize all model parameters in Gaussian mixture CDHMMs, including means, covariances, and mixture weights. We have investigated the proposed CLS approach on several benchmark speech recognition databases, including TIDIGITS, Resource Management (RM), and Switchboard. Experimental results show that the new CLS optimization method consistently outperforms the conventional EBW method in both recognition performance and convergence behavior.

Designing spatially heterogeneous strategies for control of virus spread

The spread of a virus--whether in a human population, computer network or cell-to-cell--is closely tied to the spatial (graph) topology of the interactions among the possible infectives. The authors study the problem of allocating limited control resources (e.g. quarantine or recovery resources) in these networks in a way that exploits the topological structure, so as to maximise the speed at which the virus is eliminated. For both multi-group and contact-network models for spread, these problems can be abstracted to a particular decentralised control problem for which the goal is to minimise the dominant eigenvalue of a system matrix. Explicit solutions to these problems are provided, using eigenvalue sensitivity ideas together with constrained optimisation methods employing Lagrange multipliers. The proposed design method shows that the optimal strategy is to allocate resources so as to equalise the propagation impact of each network component, as best as possible within the constraints on the resource. Finally, we show that this decentralised control approach can provide significant advantage over a homogeneous control strategy, in the context of a model for SARS transmission in Hong Kong.

A penalized nonparametric method for nonlinear constrained optimization based on noisy data

The objective of this study is to find a smooth function joining two points A and B with minimum length constrained to avoid fixed subsets. A penalized nonparametric method of finding the best path is proposed. The method is generalized to the situation where stochastic measurement errors are present. In this case, the proposed estimator is consistent, in the sense that as the number of observations increases the stochastic trajectory converges to the deterministic one. Two applications are immediate, searching the optimal path for an autonomous vehicle while avoiding all fixed obstacles between two points and flight planning to avoid threat or turbulence zones.

A nonmonotone filter trust region method for nonlinear constrained optimization

In this paper, we present a nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. Similar to Bryd–Omojokun class of algorithms, each step is composed of a quasi-normal step and a tangential step. This new method has more flexibility for the acceptance of the trial step compared to the filter methods, and requires less computational costs compared with the monotone methods. Under reasonable conditions, we give the globally convergence properties. Numerical tests are presented that confirm the efficiency of the approach.

On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization

In this paper, we present new convergence properties of the primal-dual method based on four types of augmented Lagrangian functions in the context of constrained global optimization. Convergence to a global optimal solution is first established for a basic primal-dual scheme under standard conditions. We then prove this convergence property for a modified augmented Lagrangian method using a safeguarding strategy without appealing to the boundedness assumption of the multiplier sequence. We further show that, under the same weaker conditions, the convergence to a global optimal solution can still be achieved by either modifying the multiplier updating rule or normalizing the multipliers in augmented Lagrangian methods.

A line search filter approach for the system of nonlinear equations

Some constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations.

A filter-trust-region method for simple-bound constrained optimization

In this paper we propose a filter-trust-region algorithm for solving nonlinear optimization problems with simple bounds. It extends the technique of Gould et al. [Gould, N.I.M. Sainvitu, C. and Toint, Ph.L., 2005, A filter-trust-region method for unconstrained optimization. SIAM Journal on Optimization, 16(2), 341–357.] designed for unconstrained optimization problems. The two main ingredients of the method are a filter-trust-region algorithm and a gradient-projection method. The algorithm is shown to be globally convergent to at least one first-order critical point. Numerical experiments on a large set of problems are also reported.

Optimization Method RasID-GA for Numerical Constrained Optimization Problems

This paper proposes Adaptive Random search with Intensification and Diversification combined with Genetic Algorithm (RasID-GA) for constrained optimization. In the previous work, we proposed RasID-GA which combines the best properties of RasID and Genetic Algorithm for unconstrained optimization problems. In general, it is very difficult to find an optimal solution for constrained optimization problems because their feasible solution space is very limited and they should consider the objective functions and constraint conditions. The conventional constrained optimization methods usually use penalty functions to solve given problems. But, it is generally recognized that the penalty function is hard to handle in terms of the balance between penalty functions and objective functions. In this paper, we propose a constrained optimization method using RasID-GA, which solves given problems without using penalty functions. The proposed method is tested and compared with Evolution Strategy with Stochastic Ranking using well-known 11 benchmark problems with constraints. From the Simulation results, RasID-GA can find an optimal solution or approximate solutions without using penalty functions.

Pattern Search Method for Discrete L 1–Approximation

We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical experiments seem to be encouraging.

Convergence of the Implicit Filtering Method for Constrained Optimization of Noisy Functions

In this paper, we develop convergence theory of the implicit filtering method for solving the box constrained optimization whose objective function includes a smooth term and a noisy term. It is shown that under certain assumption on the noisy function, the sequence of projected gradients on the smooth function produced by the method goes to zero. Moreover, it is shown that if the smooth function is convex and the noisy function decays near optimality, the whole sequence of iterates converges to a solution of the concerned problem and possesses the finite identification for the optimal active set under the nondegenerate assumption. Finally, preliminary numerical results are reported.

On the choice of parameters for the weighting method in vector optimization

We present a geometrical interpretation of the weighting method for constrained (finite dimensional) vector optimization. This approach is based on rigid movements which separate the image set from the negative of the ordering cone. We study conditions on the existence of such translations in terms of the boundedness of the scalar problems produced by the weighting method. Finally, using recession cones, we obtain the main result of our work: a sufficient condition under which weighting vectors yield solvable scalar problems.

Single-Diameter Technology Capable of Increasing Extended-Reach Drilling by 50%

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper OTC 17828, "Single-Diameter Technology Capable of Increasing Extended-Reach Drilling by 50%," by R. Bell, R. McKee, and E. Zwald, Enventure Global Technology, and D. Lewis, SPE, and P.V. Suryanarayana, SPE, Blade Energy Partners, prepared for the 2006 Offshore Technology Conference, Houston, 1–4 May. The combination of single-diameter technology and extended-reach drilling (ERD) can have a positive effect on capital-cost structure. Single-diameter technology provides the foundation for a significant increase in the lateral reach of many extended-reach wellbores. This extended lateral reach results in increased reservoir contact that can lead to increased production per well, which can reduce field well counts. Introduction Solid expandable tubulars (SETs) have evolved over the last few years into a proven openhole-drilling-liner and cased-hole-remedial-liner alternative to conventional technology. A well-design feasibility study was conducted as part of the front-end engineering and design for a major North Sea operator. The study was performed to evaluate the relative merits of using conventional drilling technology vs. expandable-tubular technology for lateral reach and the effect on capital efficiency and potential field development. This well-design study indicated potential lateral-reach increases of 25 to 100%. Drilling-performance and cost studies indicated that existing and planned well costs and times in the same North Sea fields could be reduced by more than U.S. $40 million or 30 to 50% of the current drilling cost and time. Expandable ERD Well Design An existing North Sea oil development project and a planned subsea gas development project were used to evaluate and quantify the lateral-reach improvements possible with SETs. An in-house program was used for drillstring mechanics, stress analysis, and fatigue analysis that included operator-provided drilling and completion data, lithology, mud parameters, torque and drag, and well designs. Historical data provided a baseline for ERD in the subject fields and a context for estimation of trouble times and expected time to drill extended-reach wells as long as 50,160 ft. The current lateral-reach record in the North Sea field is approximately 26,400 ft, with significant drilling trouble. All aspects of SETs and single-diameter liners were considered in the context of ERD beyond conventional-technology limits, including the unique force transmission during expandable-technology operations. Optimal well paths were planned by use of constrained optimization methods. Wear analysis was based on an adhesive-wear model that is the basis of all industry wear-analysis programs. Casing integrity was evaluated with the working stress design approach (deterministic design) and supplemented by probabilistic design where appropriate. Drag risk was evaluated. The base well-design model evaluated the achievable lateral reach and drilling-trouble reduction with the following.Conventional drilling technology.Conventional technology with improved drilling practices.Installation of two SET liners to preserve the desired completion size.Installation of multiple, successive single-diameter drilling liners.

Modelling and identification of an all-terrain vehicle

Nowadays the development of new systems in the field of automotive engineering, for example the active chassis, takes place entirely at the computer. A prerequisite is a validated computer model of the target vehicle. This model has to reproduce the motion behaviour of the target vehicle with sufficient precision. In general, there exist several methods to obtain such a model. The chosen method conforms to our aim to incorporate into the model as many known properties and parameters of the real vehicle as possible. In a first step this leads to a modelling of the vehicle as a multi-body model, or a rigid-body model. In a second step the structure and the parameters of the model are identified in the frequency domain by means of non-linear, constrained optimisation methods. The result is an identified and validated vehicle model, which is appropriate for the design of an active chassis at the computer.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

An affine scaling reduced preconditional conjugate gradient path method for linear constrained optimization

This paper presents an affine scaling reduced preconditional conjugate gradient path approach in association with nonmonotonic interior backtracking line search technique for the linear constrained optimization. Employing the affine scaling preconditional conjugate gradient to form the curvilinear path and using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions.

Interpretation of borehole magnetometer data for the detection and characterisation of unexploded bombs

Unexploded war-time bombs (UXB) can be found at the ground surface or buried at depths of up to 20 m, where surface-based detection methods become ineffective due to signal weakness and interference. A total-field borehole magnetometer can penetrate to such depths and collect relatively quiet data. However, conventional interpretation techniques suffer from the inherent non-uniqueness in the borehole dimension. In this paper, a constrained optimisation method is utilised for the interpretation of total-field borehole magnetometer data for the detection of deeply buried unexploded bombs. The major advantage over conventional techniques comes from the analytically-derived constraints imposed on the parameter vector by excluding non-geosensible results from consideration and hence reducing the non-uniqueness to a minimal level. A depth dependant objective function is defined to minimise the interference and measurement errors. A test site has been developed for evaluation using real world data. The interpretation results demonstrate its superior capability in handling real-world problems with high non-uniqueness. Furthermore, this method provides a way to estimate the moment strength without knowing the exact position. Together with the modelled signature data for different objects, characterisation of a particular bomb is possible from the inversion of a single total-field borehole profile.