nonlinearly constrained discrete time optimal control problems we consider a class of constrained discrete time optimal control problems we use the discrete version of the control parametrization concept together with a simple constraint transcription to devise a computational algorithm for solving this class of problems convergence analysis is given to support this numerical approach for illustration three nontrivial optimal control problems are solved using it

a semiparametric method for estimating population size for capture recapture experiments with random covariates in continuous time a semiparametric estimation procedure is proposed to model capture recapture data with the aim of estimating the population size for a closed population individuals covariates are possibly time dependent and missing at noncaptured times and may be measured with error a set of estimating equations ees based on covariate process and capture recapture data is constructed to estimate the relevant parameters and the population size these ees can be solved by an algorithm similar to an em algorithm simulation results show that the proposed procedures work better than the naive estimate in some cases they are even better than ideal estimates for which the true values of covariates are available for all captured subjects over the entire experimental period we apply the method to a capture recapture experiment on the bird species prinia flaviventris in hong kong

a new computational algorithm for functional inequality constrained optimization problems abstract in this note a computational algorithm is devised for solving a class of functional inequality constrained optimization problems based on a penalty function for illustration a numerical example is solved

a metropolis algorithm combined with hooke jeeves local search method applied to global optimization abstract a hybridization of a recently introduced metropolis algorithm named the particle collision algorithm pca and the hooke jeeves local search method is applied to a testbed of global optimization functions and to real world chemical equilibrium nonlinear systems the results obtained by this method called hjpca are compared against those achieved by two state of the art global optimization methods c grasp and global hjpca performs better than both algorithms thus demonstrating its potential for other applications

modal analysis of a nonlinear periodic structure with cyclic symmetry this paper carries out modal analysis of a nonlinear periodic structure with cyclic symme try the nonlinear normal mode nnm theory is brie y described and a computational algorithm for the nnm computation is presented the results obtained on a simpli ed model of a bladed assembly show that this system possesses a very complicated struc ture of nnms including similar and nonsimilar nnms nonlocalized and localized nnms bifurcating and internally resonant nnms modal interactions that occur without neces sarily having commensurate natural frequencies in the underlying linear system are also discussed

on root finding algorithms for complex functions with branch cuts abstract a simple and versatile method is presented which enhances the complex root finding process by eliminating branch cuts and branch points in the analyzed domain for any complex function defined by a finite number of riemann sheets a pointwise product of all the surfaces can be obtained such single valued function is free of discontinuity caused by branch cuts and branch points the roots of the new function are the same as the roots of original multi valued variety while the verification of them is much easier such approach can significantly improve the efficiency as well as the effectiveness of the root finding algorithms the validity of the presented technique is supported by the results obtained from numerical tests

the harmonic balance method with arc length continuation in rotor stator contact problems there are a variety of abnormal running conditions in rotating machinery which lead to rotor stator interaction dynamics which in turn can cause a rich mixture of effects associated with rub related phenomena these effects manifest themselves in the occurrence of multiple solutions for steady state vibration response scenarios including amplitude jumps during rotor acceleration and vibration responses at different multiple frequencies of excitation forces such as unbalance this paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non linear system under periodic excitation the algorithm also calculates the stability of the periodic solutions found marks turning and bifurcation points and follows a solution branch over varying system parameters via arc length continuation

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

robust design and the use of auxiliary variables in estimating population size for an open population nous considerons le probleme de l estimation de la taille d une population ouverte ou les donnees sont collectees sur une deuxieme periode a l interieur d une periode primaire selon un plan robuste propose par pollock 1982 une vraisemblance conditionnelle est utilisee pour estimer les parametres associes a un modele lineaire generalise pour lequel la probabilite de capture est supposee suivre une loi logistique qui depend de covariables individuelles un estimateur de type horvitz thompson est utilise pour estimer la taille de la population pour chaque periode primaire et les probabilites du survie entre les periodes primaires les proprietes asymptotiques de l estimateur propose explorees par simulation ont de bonnes proprietes un jeu de donnee attache a une etude de capture recapture de petits mammiferes conduite selon un plan robuste a dummy bottom au sein du browns park national wildlife refuge est analyse

logistic regression in capture recapture models the effect of population heterogeneity in capture recapture or dual registration models is discussed an estimator of the unknown population size based on a logistic regression model is introduced the model allows different capture probabilities across individuals and across capture times the probabilities are estimated from the observed data using conditional maximum likelihood the resulting population estimator is shown to be consistent and asymptotically normal a variance estimator under population heterogeneity is derived the finite sample properties of the estimators are studied via simulation an application to finnish occupational disease registration data is presented

an approximate decomposition algorithm for convex minimization for nonsmooth convex optimization robert mifflin and claudia sagastizabal introduce a vu space decomposition algorithm in mifflin and sagastizabal 2005 11 an attractive property of this algorithm is that if a primal dual track exists this algorithm uses a bundle subroutine with the inclusion of a simple line search it is proved to be globally and superlinearly convergent however a drawback is that it needs the exact subgradients of the objective function which is expensive to compute in this paper an approximate decomposition algorithm based on proximal bundle type method is introduced that is capable to deal with approximate subgradients it is shown that the sequence of iterates generated by the resulting algorithm converges to the optimal solutions of the problem numerical tests emphasize the theoretical findings

estimation in closed capture recapture models when covariates are missing at random individual covariates are commonly used in capture recapture models as they can provide important information for population size estimation however in practice one or more covariates may be missing at random for some individuals which can lead to unreliable inference if records with missing data are treated as missing completely at random we show that in general such a naive complete case analysis in closed capture recapture models with some covariates missing at random underestimates the population size we develop methods for estimating regression parameters and population size using regression calibration inverse probability weighting and multiple imputation without any distributional assumptions about the covariates we show that the inverse probability weighting and multiple imputation approaches are asymptotically equivalent we present a simulation study to investigate the effects of missing covariates and to evaluate the performance of the proposed methods we also illustrate an analysis using data on the bird species yellow bellied prinia collected in hong kong

the analysis of group truncated binary data with random effects injury severity in motor vehicle accidents the analysis of group truncated binary data has been previously considered by o neill and barry 1995b biometrics 51 533 541 where the analysis assumed that responses within each group were independent in this paper we consider the analysis of such data when there is group level heterogeneity a generalized linear mixed model is hypothesized to model the response and maximum likelihood estimates are derived for the truncated case a score test is derived to test for heterogeneity finally the method is applied to a set of traffic accident data

estimating population size for a continuous time frailty model with covariates in a capture recapture study a continuous time frailty capture recapture model is proposed for estimating population size of a closed population with the use of observed covariates to explain individuals heterogeneity in presence of a random effect a conditional likelihood approach is used to derive the estimate of parameters and the horvitz thompson estimator is adopted to estimate the unknown population size asymptotic normality of the estimates is obtained simulation results and a real example show that the proposed method works satisfactorily

a general theory for modeling capture recapture data from a closed population a general theory for estimating the size of a closed population from multiple recapture data is presented this theory is easily extended to open population models for multiple recapture data estimation is based on a log linear model developed for modeling dependent capture recapture data when capture probabilities vary temporally with behavioral response and are heterogeneous among animals models for complete capture history data are developed along with the first log linear models for removal data the maximum likelihood estimator of the model parameters along with the estimated covariance matrix are presented

minimizing control variation in discrete time optimal control problems for a real practical system a large fluctuation in the control signal is highly undesirable to address this undesirable situation we investigate a discrete time optimal control problem subject to terminal state and all time step constraints on the state and control where the cost function is the sum of terminal cost and the variation of the control signal the variation of the control signal is expressed in terms of absolute value functions and hence is non smooth by a novel smooth transformation and the constraint transcription technique this problem is approximated by a constrained discrete time optimal control with the new cost function involves only smooth functions a gradient based computational method is then derived which is supported by rigorous convergence analysis two examples are provided to demonstrate the effectiveness and advantages of the proposed method we present a gradient based method for discrete time optimal control problems the cost function is the sum of terminal cost and the variation of control signal a smooth transformation and the constraint transcription technique are used two examples are provided to demonstrate the feasibility of the method

maximization of the vibration amplitude and bifurcation analysis of nonlinear systems using the constrained optimization shooting method abstract an original method for calculating the maximum vibration amplitude of periodic solutions of nonlinear systems is presented the problem of determining the worst maximum vibration is transformed into a nonlinear optimization problem the shooting method and the floquet theory are selected to construct the general nonlinear equality and inequality constraints the resulting constrained maximization problem is then solved by using the multistart algorithm finally the effectiveness and ability of the proposed approach are illustrated through two numerical examples numerical examples show that the proposed method can give results with higher accuracy as compared with numerical results obtained by a parameter continuation method and the ability of the present method is also demonstrated

a comparison of classical and high dimensional harmonic balance approaches for a duffing oscillator the present study focuses on a novel harmonic balance formulation which is much easier to implement than the standard classical harmonic balance method for complex nonlinear mathematical models and algorithms both harmonic balance approaches are applied to duffing s oscillator to demonstrate the advantages and disadvantages of the two approaches a fundamental understanding of the difference between these two methods is achieved and the properties of each method are analyzed in detail

non linear free periodic vibrations of open cylindrical shallow shells this paper is concerned with the non linear free periodic vibrations of thin open cylindrical and shallow shells vibrating in the geometrically non linear regime a multi degree of freedom model with hierarchical basis functions is adopted and the principle of the virtual work is used to define the time domain equations of motion these equations are transformed into the frequency domain by the harmonic balance method and are finally solved by an arc length continuation method shells of different thicknesses and of different curvature radius are analysed and the variation of the non linear natural frequencies of these shells with the vibration amplitude are investigated in some detail the variation of the mode shapes with the vibration amplitude is demonstrated it is found that both softening and hardening spring effects occur and that the number of couplings between vibration modes is rather large in undamped shells

open capture recapture models with heterogeneity ii jolly seber model summary estimation of abundance is important in both open and closed population capture recapture analysis but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates this article defines and develops a suite of open population capture recapture models using finite mixtures to model heterogeneity of capture and survival probabilities model comparisons and parameter estimation use likelihood based methods a real example is analyzed and simulations are used to check the main features of the heterogeneous models especially the quality of estimation of abundance survival recruitment and turnover the two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present

adjusting for nonresponse bias using logistic regression summary a method of adjustment for nonresponse is considered no information about the nonrespondents is required but the respondents are assumed to answer all questions of interest one or more call backs are assumed the probabilities of response are represented by a logistic regression model in which variables in the survey are explanatory variables the probabilities are estimated using a modified conditional maximum likelihood approach based on the respondents the estimated probabilities are used in a horvitzthompson type estimator to reduce bias in the estimation of sample moments simulations suggest that the method reduces the mean squared error of estimation when response probabilities depend strongly on variables in the survey

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

new modified multi level residue harmonic balance method for solving nonlinearly vibrating double beam problem abstract in this study a new modified multi level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams although numerous nonlinear beam or linear double beam problems have been tackled and solved there have been few studies of this nonlinear double beam problem the geometric nonlinear formulations for a double beam model are developed the main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level this heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method the proposed method can generate the higher level nonlinear solutions that are neglected by the previous modified harmonic balance method the results from the proposed method agree reasonably well with those from the classical harmonic balance method the effects of damping axial force and excitation magnitude on the nonlinear vibrational behaviour are examined

accommodating unmodeled heterogeneity in double observer distance sampling surveys mark recapture models applied to double observer distance sampling data neglect the information on relative detectability of objects contained in the distribution of observed distances a difference between the observed distribution and that predicted by the mark recapture model is symptomatic of a failure of the assumption of zero correlation between detection probabilities implicit in the mark recapture model we develop a mark recapture based model that uses the observed distribution to relax this assumption to zero correlation at only one distance we demonstrate its usefulness in coping with unmodeled heterogeneity using data from an aerial survey of crabeater seals in the antarctic

the use of auxiliary variables in capture recapture and removal experiments the dependence of animal capture probabilities on auxiliary variables is an important practical problem which has not been considered in the development of estimation procedures for capturerecapture and removal experiments in this paper the linear logistic binary regression model is used to relate the probability of capture to continuous auxiliary variables the auxiliary variables could be environmental quantities such as air or water temperature or characteristics of individual animals such as body length or weight maximum likelihood estimators of the population parameters are considered for a variety of models which all assume a closed population testing between models is also considered the models can also be used when one auxiliary variable is a measure of the effort expended in obtaining the sample

maximum empirical likelihood estimation for abundance in a closed population from capture recapture data summarycapture recapture experiments are widely used to collect data needed for estimating the abundance of a closed population to account for heterogeneity in the capture probabilities huggins 1989 and alho 1990 proposed a semiparametric model in which the capture probabilities are modelled parametrically and the distribution of individual characteristics is left unspecified a conditional likelihood method was then proposed to obtain point estimates and wald type confidence intervals for the abundance empirical studies show that the small sample distribution of the maximum conditional likelihood estimator is strongly skewed to the right which may produce wald type confidence intervals with lower limits that are less than the number of captured individuals or even are negative in this paper we propose a full empirical likelihood approach based on huggins and alho s model we show that the null distribution of the empirical likelihood ratio for the abundance is asymptotically chi squared with one degree of freedom and that the maximum empirical likelihood estimator achieves semiparametric efficiency simulation studies show that the empirical likelihood based method is superior to the conditional likelihood based method its confidence interval has much better coverage and the maximum empirical likelihood estimator has a smaller mean square error we analyse three datasets to illustrate the advantages of our empirical likelihood approach

log linear models for capture recapture summary log linear models are developed for capture recapture experiments and their advantages and disadvantages discussed ways in which they can be extended sometimes with only partial success to open populations subpopulations trap dependence and long chains of recapture periods are presented the use of residual patterns and analysis of subsets of data to identify behavioural patterns and acceptable models is emphasised and illustrated with two examples 1 capture recapture the biological problem with which we are concerned is that of estimating the parameters of a free living population of unknown size from a sequence of s samples in each of which any individual either is or is not observed the models in this paper require that each animal be marked naturally or artificially in such a way that we can observe the numbers of animals which have any particular pattern of being or not being observed through the sequence of samples there are t 2s 1 different observable patterns which we shall refer to as capture histories although there is no requirement for physical capture and denote each pattern by a sequence of l s and 2 s representing respectively seen or not seen in a particular sample a general pattern of capture history will be denoted a with ra the number of individuals observed to have this pattern thus for example with s 3 samples and a 121 r 2 is the number of animals seen in the first and third samples but not in the second the pattern with all 2 s is by definition unobservable in general the population will be subject to demographic change by birth or immigration and by death or emigration the simplest assumption for the response of an animal to the observer one which underlies the classical petersen schnabel or jolly seber estimators is that every animal alive in the population at a sampling time has the same probability of being observed this probability may vary from one sample to another or be constant over all or a number of samples if this assumption fails it may do so for either or both of two reasons the first is that of trap dependence the probability of an individual being observed in a sample depending on its past history of capture the second is that of heterogeneity between individuals who because of differences in their behaviour or in where they live inherently have different probabilities of being observed in any sample the basic idea of heterogeneity refers to properties of individuals which remain constant over time but individual animals may also have time varying behaviour the aspect most commonly considered being temporary departure of an individual from the population various excellent texts describe theoretical and practical aspects of capture recapture notably the comprehensive one by seber 1982 the introduction by begon 1979 the

a one parameter filled function method applied to nonsmooth constrained global optimization in this paper we propose a filled function method for solving nonsmooth constrained global optimization problems based on a new definition of the filled function a more practical one parameter filled function is constructed which overcomes some drawbacks of the previous filled functions then a corresponding algorithm is presented it attains a local minimizer by implementing a local search procedure and finds a better local minimizer gradually by optimizing the filled function constructed on the minimizer previously found by repeating these steps a global minimizer is obtained numerical experiments are presented to show the practicability of the proposed filled function method in the end extension conceivable applications are given in order to evaluate the merits of this method

a new filled function method for constrained nonlinear equations abstract in this paper we extend the filled function method proposed in lin et al 2009 10 to solve the constrained system of nonlinear equations and we propose two methods to find a solution of such a system finally the efficiency of the present method is illustrated through some examples

the instability of the hocking stewartson pulse and its geometric phase in the hopf bundle this work demonstrates an innovative numerical method for counting and locating eigenvalues with the evans function utilizing the geometric phase in the hopf bundle the technique calculates the winding of the evans function about a contour in the spectral plane describing the eigenvalues enclosed by the contour for the hocking stewartson pulse of the complex ginzburg landau equation locating eigenvalues with the geometric phase in the hopf bundle was proposed by way 2009 and proven by grudzien et al 2016 way demonstrated his proposed method for the hocking stewartson pulse and this manuscript redevelops this example as in the proof of the method in grudzien et al 2016 modifying his numerical shooting argument and introduces new numerical results concerning the phase transition

periodic geometrically nonlinear free vibrations of circular plates abstract the geometrically nonlinear free vibrations of thin isotropic circular plates are investigated using a multi degree of freedom model which is based on thin plate theory and on von karman s nonlinear strain displacement relations the middle plane in plane displacements are included in the formulation and the common axisymmetry restriction is not imposed the equations of motion are derived by the principle of the virtual work and an approximated model is achieved by assuming that the in plane and transverse displacement fields are given by weighted series of spatial functions these spatial functions are based on hierarchical sets of polynomials which have been successfully used in p version finite elements for beams and rectangular plates and on trigonometric functions employing the harmonic balance method the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method convergence with the number of shape functions and of harmonics is analysed the numerical results obtained are presented and compared with available published results it is shown that the hierarchical sets of functions provide good results with a small number of degrees of freedom internal resonances are found and the ensuing multimodal oscillations are described

mixture regression models for closed population capture recapture data in capture recapture studies the use of individual covariates has been recommended to get stable population estimates however some residual heterogeneity might still exist and ignoring such heterogeneity could lead to underestimating the population size n in this work we explore two new models with capture probabilities depending on both covariates and unobserved random effects to estimate the size of a population inference techniques including horvitz thompson estimate and confidence intervals for the population size are derived the selection of a particular model is carried out using the akaike information criterion aic first we extend the random effect model of darroch et al 1993 journal of american statistical association 88 1137 1148 to handle unit level covariates and discuss its limitations the second approach is a generalization of the traditional zero truncated binomial model that includes a random effect to account for an unobserved heterogeneity this approach provides useful tools for inference about n since key quantities such as moments likelihood functions and estimates of n and their standard errors have closed form expressions several models for the unobserved heterogeneity are available and the marginal capture probability is expressed using the logit and the complementary log log link functions the sensitivity of the inference to the specification of a model is also investigated through simulations a numerical example is presented we compare the performance of the proposed estimator with that obtained under model mh of huggins 1989 biometrika 76 130 140

a filled function method for minimizing control variation in constrained discrete time optimal control problems abstract this paper considers a discrete time optimal control problem subject to terminal state constraints and all time step inequality constraints where the cost function involves a terminal cost a summation cost and a penalty on the change of the control action the variation of the control signal and the all time step constraints are non smooth functions thus this optimal control problem is formulated as a non smooth constrained optimization problem however it is nonconvex and hence it may have many local minimum points thus a filled function method is introduced in conjunction with local optimization techniques to solve this non smooth and nonconvex constrained optimization problem for illustration two numerical examples are presented and solved using the proposed approach

bias reduction for multiple recapture estimators of closed population size a bias correction for multiple recapture sampling is proposed the correction is similar to chapman s 1951 university of california publication in statistics 1 131 160 correction of the lincoln petersen estimator of population size small sample properties of the modified population size estimator are examined using monte carlo simulation substantial reductions in estimator bias and variance are obtained with the modified estimator

some practical aspects of a conditional likelihood approach to capture experiments the use of conditional likelihood methods in the analysis of capture data allows the modeling of capture probabilities in terms of observable characteristics of the captured individuals and the trapping occasions the resulting models may then be used to estimate the size of the population here the use of conditional likelihood procedures to construct models for capture probabilities is discussed and illustrated by an example

a limited memory quasi newton trust region method for box constrained optimization by means of wolfe conditions strategy we propose a quasi newton trust region method to solve box constrained optimization problems this method is an adequate combination of the compact limited memory bfgs and the trust region direction while the generated point satisfies the wolfe conditions and therefore maintains a positive definite approximation to the hessian of the objective function the global convergence and the quadratic convergence of this method are established under suitable conditions finally we compare our algorithms iwtral and ibwtral with an active set trust region algorithm astral xu and burke 2007 on the cutest box constrained test problems presented by gould et al 2015 numerical results show that the presented method is competitive and totally interesting for solving box constrained optimization