Asymptotically Optimal Empirical Bayes Estimation of Parameter for Scale-exponential Family under PA Samples

The Bayes estimator of the parameter is obtained for the scale exponential family in the case of identically distributed and positively associated（PA） samples under weighted square loss function.We construct the empirical Bayes（EB） estimator and prove it is asymptotic optimal.

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.

Optimal Design of Multiple Stress Constant Accelerated Life Test Plan on Non-rectangle Test Region

For optimal design of constant stress accelerated life test（CSALT） with two-stress, if the stresses could not reach the highest levels simultaneously, the test region becomes non-rectangular. For optimal CSALT design on non-rectangle test region, the present method is only focused on non-rectangle test region with simple boundary, and the optimization algorithm is based on experience which can not ensure to obtain the optimal plan. In this paper, considering the linear-extreme value model and the optimization goal to minimize the variance of lifetime estimate under normal stress, the optimal design method of two-stress type-I censored CSALT plan on general non-rectangular test region is proposed. First, two properties of optimal test plans are proved and the relationship of all the optimal test plans is determined analytically. Then, on the basis of the two properties, the optimal problem is simplified and the optimal design method of two-stress CSALT plan on general non-rectangular test region is proposed. Finally, a numerical example is used to illustrate the feasibility and effectiveness of the method, The result shows that the proposed method could obtain the optimal test plan on non-rectangular test regions with arbitrary boundaries. This research provides the theory and method for two-stress optimal CSALT planning on non-rectangular test regions.

THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u 〉 0, x ∈ Ω, u｜δΩ =＋∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞）, g（0） = g＇（0） = 0, and there exists p 〉 1, such that lim g（sξ）/g（s）=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α（Ω） is non-negative non-trivial in D which may be singular on the boundary.

Numerical solutions of second order initial value problems of Bratu-type via optimal homotopy asymptotic method

We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.

An Optimal Design of Accelerated Degradation Tests Based on Degradation Performance

This paper mainly talks about the relationship between an optimal design of accelerated degradation tests and the degradation performance. When there is a linear relationship between the parameter of distribution and the critical values, a special pattern of accelerated degradation tests is presented by taking the critical values as accelerated variable. And the optimal test plan is obtained by minimizing the asymptotic variance of the MLE of the parameter of distribution. Finally, a numerical example is presented to illustrate the procedures of the test plan.

Optimal Weights in Nonparametric Analysis of Clustered ROC Curve Data

In diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. Within-cluster correlations need to be taken into account when analyzing such clustered data. A nonparametric method has been proposed by Obuchowski (1997) to estimate the Receiver Operating Characteristic curve area (AUC) for such clustered data. However, Obuchowski’s estimator gives equal weight to all pairwise rankings within and between cluster. In this paper, we modify Obuchowski’s estimate by allowing weights for the pairwise rankings vary across clusters. We consider the optimal weights for estimating one AUC as well as two AUCs’ difference. Our results in this paper show that the optimal weights depends on not only the within-patient correlation but also the proportion of patients that have both unaffected and affected units. More importantly, we show that the loss of efficiency using equal weight instead of our optimal weights can be severe when there is a large within-cluster correlation and the proportion of patients that have both unaffected and affected units is small.

OPTIMAL POWER ALLOCATION WITH AF AND SDF STRATEGIES IN DUAL-HOP COOPERATIVE MIMO NETWORKS

Dual-hop cooperative Multiple-Input Multiple-Output (MIMO) network with multi-relay cooperative communication is introduced. Power allocation problem with Amplify-and-Forward (AF) and Selective Decode-and-Forward (SDF) strategies in multi-node scenario are formulated and solved respectively. Optimal power allocation schemes that maximize system capacity with AF strategy are presented. In addition, optimal power allocation methods that minimize asymptotic Symbol Error Rate (SER) with SDF cooperative protocol in multi-node scenario are also proposed. Furthermore, performance comparisons are provided in terms of system capacity and approximate SER. Numerical and simulation results confirm our theoretical analysis. It is revealed that, maximum system capacity could be obtained when powers are allocated optimally with AF protocol, while minimization of system's SER could also be achieved with optimum power allocation in SDF strategy. In multi-node scenario, those optimal power allocation algorithms are superior to conventional equal power allocation schemes.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Optimal regularity of positive solutions of the Hénon-Hardy equation and related equations

We present a new method to determine the optimal regularity of positive solutions u∈C^(4)(Ω\{0})∩C^(0)(Ω) of the Hénon-Hardy equation,i.e.,Δ^(2)u=|x|^(α)u^(p)inΩ,(0,1) where Ω■RN(N≥4) is a bounded smooth domain with 0∈Ω,α>-4,and p∈R.It is clear that 0 is an isolated singular point of solutions of(0.1) and the optimal regularity of u in Ω relies on the parameter α.It is also important to see that the regularity of u at x=0 determines the regularity of u in Ω.We first establish asymptotic expansions up to arbitrary orders at x=0 of prescribed positive solutions u ∈C^(4)(Ω{0}) ∩ C^(0)(Ω)of(0.1).Then we show that the regularity at x=0 of each positive solution u of(0.1) can be determined by some terms in asymptotic expansions of the related positive radial solution of the equation(0.1) with Ω=B,where B is the unit ball of R^(N).The main idea works for more general equations with singular weights.

Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization

Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.

A Stable Analytical Solution Method for Car-Like Robot Trajectory Tracking and Optimization

In this paper, the car-like robot kinematic model trajectory tracking and control problem is revisited by exploring an optimal analytical solution which guarantees the global exponential stability of the tracking error. The problem is formulated in the form of tracking error optimization in which the quadratic errors of the position, velocity, and acceleration are minimized subject to the rear-wheel car-like robot kinematic model. The input-output linearization technique is employed to transform the nonlinear problem into a linear formulation. By using the variational approach, the analytical solution is obtained, which is guaranteed to be globally exponentially stable and is also appropriate for real-time applications. The simulation results demonstrate the validity of the proposed mechanism in generating an optimal trajectory and control inputs by evaluating the proposed method in an eight-shape tracking scenario.

Acceleration Factor Harmonious Particle Swarm Optimizer

A Particle Swarm Optimizer （PSO） exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and restrictive conditions, which can affect the performance of the algorithm. In this paper, the sufficient conditions for the asymptotic stability of an acceleration factor and inertia weight are deduced, the value of the inertia weight w is enhanced to （ 1, 1）. Furthermore a new adaptive PSO algorithm - Acceleration Factor Harmonious PSO （AFHPSO） is proposed, and is proved to be a global search algorithm. AFHPSO is used for the parameter design of a fuzzy controller for a linear motor driving servo system. The performance of the nonlinear model for the servo system demonstrates the effectiveness of the optimized fuzzy controller and AFHPSO.

THE ASYMPTOTICALLY OPTIMAL EMPIRICALBAYES ESTIMATION IN ONE WAY ANOVA MODEL

Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2). By using the kernel estimation of multivariate density function and its partial derivatives and making use of the estimators of nuisance parameters μ and σ2, we construct the empirical Bayes (EB) estimators of parameter vector α = (α1,…，αa)T. Under the existence condition of the second order moment on prior distribution, we obtain their asymptotic optimality.

Common model analysis and improvement of particle swarm optimizer

Particle swarm optimizer （PSO）, a new evolutionary computation algorithm, exhibits good performance for optimization problems, although PSO can not guarantee convergence of a global minimum, even a local minimum. However, there are some adjustable parameters and restrictive conditions which can affect performance of the algorithm. In this paper, the algorithm are analyzed as a time-varying dynamic system, and the sufficient conditions for asymptotic stability of acceleration factors, increment of acceleration factors and inertia weight are deduced. The value of the inertia weight is enhanced to （-1, 1）. Based on the deduced principle of acceleration factors, a new adaptive PSO algorithm- harmonious PSO （HPSO） is proposed. Furthermore it is proved that HPSO is a global search algorithm. In the experiments, HPSO are used to the model identification of a linear motor driving servo system. An Akaike information criteria based fitness function is designed and the algorithms can not only estimate the parameters, but also determine the order of the model simultaneously. The results demonstrate the effectiveness of HPSO.

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

A new hybrid MMA-MGCMMA （HMM） algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes （MMA） algorithm and the modified globally convergent version of the method of moving asymptotes （MGCMMA） algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.

Relevant Region sampling strategy with adaptive heuristic for asymptotically optimal path planning

Sampling-based planning algorithm is a powerful tool for solving planning problems in highdimensional state spaces.In this article,we present a novel approach to sampling in the most promising regions,which significantly reduces planning time-consumption.The RRT#algorithm defines the Relevant Region based on the cost-to-come provided by the optimal forward-searching tree.However,it uses the cumulative cost of a direct connection between the current state and the goal state as the cost-to-go.To improve the path planning efficiency,we propose a batch sampling method that samples in a refined Relevant Region with a direct sampling strategy,which is defined according to the optimal cost-to-come and the adaptive cost-to-go,taking advantage of various sources of heuristic information.The proposed sampling approach allows the algorithm to build the search tree in the direction of the most promising area,resulting in a superior initial solution quality and reducing the overall computation time compared to related work.To validate the effectiveness of our method,we conducted several simulations in both SE(2)and SE(3)state spaces.And the simulation results demonstrate the superiorities of proposed algorithm.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.