Co-salient object detection with iterative purification and predictive optimization

Background Co-salient object detection(Co-SOD)aims to identify and segment commonly salient objects in a set of related images.However,most current Co-SOD methods encounter issues with the inclusion of irrelevant information in the co-representation.These issues hamper their ability to locate co-salient objects and significantly restrict the accuracy of detection.Methods To address this issue,this study introduces a novel Co-SOD method with iterative purification and predictive optimization(IPPO)comprising a common salient purification module(CSPM),predictive optimizing module(POM),and diminishing mixed enhancement block(DMEB).Results These components are designed to explore noise-free joint representations,assist the model in enhancing the quality of the final prediction results,and significantly improve the performance of the Co-SOD algorithm.Furthermore,through a comprehensive evaluation of IPPO and state-of-the-art algorithms focusing on the roles of CSPM,POM,and DMEB,our experiments confirmed that these components are pivotal in enhancing the performance of the model,substantiating the significant advancements of our method over existing benchmarks.Experiments on several challenging benchmark co-saliency datasets demonstrate that the proposed IPPO achieves state-of-the-art performance.

Iterative Methods for Solving the Nonlinear Balance Equation with Optimal Truncation

Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.

Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method

In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.

Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems

Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.

Nonlinear Algebraic Equations Solved by an Optimal Splitting-Linearizing Iterative Method

How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).

An Iterative Method for Optimal Feedback Control and Generalized HJB Equation

Abstract--In this paper, a new iterative method is proposed to solve the generalized Hamilton-Jacobi-Bellman （GHJB） equation through successively approximate it. Firstly, the GHJB equation is converted to an algebraic equation with the vector norm, which is essentially a set of simultaneous nonlinear equations in the case of dynamic systems. Then, the proposed algorithm solves GHJB equation numerically for points near the origin by considering the linearization of the non-linear equations under a good initial control guess. Finally, the procedure is proved to converge to the optimal stabilizing solution with respect to the iteration variable. In addition, it is shown that the result is a closed-loop control based on this iterative approach. Illustrative examples show that the update control laws will converge to optimal control for nonlinear systems. Index Terms--Generalized Hamilton-Jacobi-Bellman （HJB） equation, iterative method, nonlinear dynamic system, optimal control.

Parametric Iteration Method for Solving Linear Optimal Control Problems

This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of functions which converges to the exact solution of problem. Our emphasis will be on an auxiliary parameter which directly affects on the rate of convergence. Comparison of PIM and the Variational Iteration Method (VIM) is given to show the preference of PIM over VIM. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.

AN ITERATIVE ALGORITHM FOR OPTIMAL DESIGN OF NON-FREQUENCY-SELECTIVE FIR DIGITAL FILTERS

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response(FIR) digital filters based on the windowing method.Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter,the key idea of the algorithm is minimizing the approximation error by succes-sively modifying the design result through an iterative procedure under the condition of a fixed window length.In the iterative procedure,the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration.Because the approximation error can be specified variably,the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain.A design example is employed to illustrate the efficiency of the algorithm.

Newton, Halley, Pell and the Optimal Iterative High-Order Rational Approximation of √<span style='margin-left:-2px;margin-right:2px;border-top:1px solid black'>N</span>

In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.

Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation

We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.

Higher Order Iteration Schemes for Unconstrained Optimization

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point;then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory;it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this paper gives a global convergence analysis for schemes associated with the quasi-Newton updates. In our computational experiments, the new schemes using DFP and BFGS updates outperformed their conventional counterparts on a set of standard test problems.

基于Iterative映射和单纯形法的改进灰狼优化算法

为了解决基本灰狼优化算法(GWO)依赖初始种群和求解精度不高的问题,提出一种基于Iterative映射和单纯形法的改进灰狼优化算法(SMIGWO)。该算法利用混沌Iterative映射产生初始灰狼种群,增强全局搜索过程中的种群多样性;采用逆不完全Γ函数更新收敛因子,以平衡算法的全局搜索和局部搜索能力;利用单纯形法的反射、扩张和收缩操作对当前较差个体进行改进,避免算法陷入局部最优。对10个测试函数进行仿真实验,数值结果表明,与基本GWO算法、Square GWO算法、非线性收敛因子的GWO(NGWO)算法、混合GWO(HGWO)算法、粒子群优化算法(PSO)、细菌觅食算法(BFA)和引力搜索算法(GSA)相比,改进的灰狼优化算法求解精度更高,稳定性更好。

An Approach of Distributed Joint Optimization for Cluster-based Wireless Sensor Networks

Wireless sensor networks (WSNs) are energyconstrained, so energy saving is one of the most important issues in typical applications. The clustered WSN topology is considered in this paper. To achieve the balance of energy consumption and utility of network resources, we explicitly model and factor the effect of power and rate. A novel joint optimization model is proposed with the protection for cluster head. By the mean of a choice of two appropriate sub-utility functions, the distributed iterative algorithm is obtained. The convergence of the proposed iterative algorithm is proved analytically. We consider general dual decomposition method to realize variable separation and distributed computation, which is practical in large-scale sensor networks. Numerical results show that the proposed joint optimal algorithm converges to the optimal power allocation and rate transmission, and validate the performance in terms of prolonging of network lifetime and improvement of throughput. © 2014 Chinese Association of Automation.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

New Optimal Newton-Householder Methods for Solving Nonlinear Equations and Their Dynamics

The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.

Study on the Application of Iterative Learning Control to Terminal Control of Linear Time-varying Systems

An iterative learning control algorithm based on shifted Legendre orthogonal polynomials is proposed to address the terminal control problem of linear time-varying systems. First, the method parameterizes a linear time-varying system by using shifted Legendre polynomials approximation. Then, an approximated model for the linear time-varying system is deduced by employing the orthogonality relations and boundary values of shifted Legendre polynomials. Based on the model, the shifted Legendre polynomials coefficients of control function are iteratively adjusted by an optimal iterative learning law derived. The algorithm presented can avoid solving the state transfer matrix of linear time-varying systems. Simulation results illustrate the effectiveness of the proposed method.

PARALLEL QUASI-CHEBYSHEV ACCELERATION TO NONOVERLAPPING MULTISPLITTING ITERATIVE METHODS BASED ON OPTIMIZATION

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonover- lapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m opti- mization models are parallelly treated in m different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, the numeri- cal examples show that the parallel quasi-Chebyshev technique can significantly accelerate the nonoverlapping multisplitting iterative method.

ITER馈线S弯结构的应力分析和优化设计

根据能量方法原理,通过单位力法和卡氏定理分析方法,理论计算得出了给定位移变形条件下沿S弯的弯矩、应力分布。分析表明,沿S弯结构的应力主要由热收缩变形产生,但重力影响也不可忽略,考虑重力影响后沿S弯最大应力较不考虑重力时增大了10%。根据该理论原理编程计算发现,在S弯高度受限的条件下,圆弧段半径越小,结构最大应力越小,实际设计中可根据强度要求结合加工工艺选择合适的圆弧半径。该分析方法为有效优化结构设计提供了理论指导。

A Least-squares-based Iterative Method with Better Convergence for PF/OPF in Integrated Transmission and Distribution Networks

The limitations of the conventional master-slavesplitting(MSS)method,which is commonly applied to power flow and optimal power flow in integrated transmission and distribution(I-T&D)networks,are first analyzed.Considering that the MSS method suffers from a slow convergence rate or even divergence under some circumstances,a least-squares-based iterative(LSI)method is proposed.Compared with the MSS method,the LSI method modifies the iterative variables in each iteration by solving a least-squares problem with the information in previous iterations.A practical implementation and a parameter tuning strategy for the LSI method are discussed.Furthermore,a LSI-PF method is proposed to solve I-T&D power flow and a LSIheterogeneous decomposition(LSI-HGD)method is proposed to solve optimal power flow.Numerical experiments demonstrate that the proposed LSI-PF and LSI-HGD methods can achieve the same accuracy as the benchmark methods.Meanwhile,these LSI methods,with appropriate settings,significantly enhance the convergence and efficiency of conventional methods.Also,in some cases,where conventional methods diverge,these LSI methods can still converge.