A rank-one algorithm for unconstrained function minimization

A rank-one algorithm is presented for unconstrained function minimization. The algorithm is a modified version of Davidon's variance algorithm and incorporates a limited line search. It is shown that the algorithm is a descent algorithm; for quadratic forms, it exhibits finite convergence, in certain cases. Numerical studies indicate that it is considerably superior to both the Davidon-Fletcher-Powell algorithm and the conjugate-gradient algorithm.     

A DERIVATIVE-FREE ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.     

An effective hybrid algorithm for computing symbolic determinants

A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19].     

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The IPSP algorithm is an efficient algorithm for computing maximum likelihood estimation of Gaussian graphical models. It first divides clique marginals of graphical models into several groups, and then it adjusts clique marginals in each group locally. This paper uses the IIPS algorithm on junction tree to replace local adjustment on each group in the IPSP algorithm and propose a resulting algorithm called IPSP-JT to reduce the complexity of the IPSP algorithm. Moreover, we give a graph with minimum edges used by IIPS to adjust locally, and we prove its existence and uniqueness and construct a local junction tree. Numerical experiments show that the IPSP-JT algorithm runs faster than the IPSP algorithm for large Gaussian graphical models.     

Nonlinear Smoothing and the EM Algorithm for Positive Integral Equations of the First Kind

We study a modification of the EMS algorithm in which each step of the EMS algorithm is preceded by a nonlinear smoothing step of the form , where S is the smoothing operator of the EMS algorithm. In the context of positive integral equations (à la positron emission tomography) the resulting algorithm is related to a convex minimization problem which always admits a unique smooth solution, in contrast to the unmodified maximum likelihood setup. The new algorithm has slightly stronger monotonicity properties than the original EM algorithm. This suggests that the modified EMS algorithm is actually an EM algorithm for the modified problem. The existence of a smooth solution to the modified maximum likelihood problem and the monotonicity together imply the strong convergence of the new algorithm. We also present some simulation results for the integral equation of stereology, which suggests that the new algorithm behaves roughly like the EMS algorithm. Accepted 1 April 1997     

An Extension of Least Angle Regression Based on the Information Geometry of Dually Flat Spaces

We extend the least angle regression algorithm using the information geometry of dually flat spaces. The extended least angle regression algorithm is used for estimating parameters in generalized linear regression, and it can be also used for selecting explanatory variables. We use the fact that a model manifold of an exponential family is a dually flat space. In estimating parameters, curves corresponding to bisectors in the Euclidean space play an important role. Originally, the least angle regression algorithm is used for estimating parameters and selecting explanatory variables in linear regression. It is an efficient algorithm in the sense that the number of iterations is the same as the number of explanatory variables. We extend the algorithm while keeping this efficiency. However, the extended least angle regression algorithm differs significantly from the original algorithm. The extended least angle regression algorithm reduces one explanatory variable in each iteration while the original algorithm increases one explanatory variable in each iteration. We show results of the extended least angle regression algorithm for two types of datasets. The behavior of the extended least angle regression algorithm is shown. Especially, estimates of parameters become smaller and smaller, and vanish in turn.     

一种新的双模式盲均衡算法研究

针对恒模算法(CMA)收敛速度较慢、收敛后均方误差较大的缺点,提出一种新的双模式盲均衡算法.在算法初期,利用能快速收敛的归一化恒模算法(NCMA)进行冷启动,在算法收敛后切换到判决引导(DD-LMS)算法,减少误码率.计算机仿真表明,提出的新算法有较快的收敛速度和较低的误码率.     

An alternative to the Bathe algorithm

This paper presents a new composite sub-steps algorithm for solving reliable numerical responses in structural dynamics. The newly developed algorithm is a two sub-steps, second-order accurate and unconditionally stable implicit algorithm with the same numerical properties as the Bathe algorithm. The detailed analysis of the stability and numerical accuracy is presented for the new algorithm, which shows that its numerical characteristics are identical to those of the Bathe algorithm. Hence, the new sub-steps scheme could be considered as an alternative to the Bathe algorithm. Meanwhile, the new algorithm possesses the following properties: (a) it produces the same accurate solutions as the Bathe algorithm for solving linear and nonlinear problems; (b) it does not involve any artificial parameters and additional variables, such as the Lagrange multipliers; (c) The identical effective stiffness matrices can be obtained inside two sub-steps; (d) it is a self-starting algorithm. Some numerical experiments are given to show the superiority of the new algorithm and the Bathe algorithm over the dissipative CH-α algorithm and the non-dissipative trapezoidal rule.     

一类特征值反问题(IEP)的基于矩阵方程的Ulm型算法

应用求解算子方程的Ulm方法构造了求解一类矩阵特征值反问题（IEP）的新算法.所给算法避免了文献[Aishima K.,A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems,Linear Algebra and its Applications,2018,542：310-33]中算法在每次迭代中要求解一个线性方程组的不足,证明了在给定谱数据互不相同的条件下所给算法具有根收敛意义下的二次收敛性.数值实验表明本文所给算法在矩阵阶数较大时计算效果优于上文所给算法.     

A POLYNOMIAL PREDICTOR-CORRECTOR INTERIOR-POINT ALGORITHM FOR CONVEX QUADRATIC PROGRAMMING

This article presents a polynomial predictor-corrector interior-point algorithm for convex quadratic programming based on a modified predictor-corrector interior-point algorithm. In this algorithm, there is only one corrector step after each predictor step, where Step 2 is a predictor step and Step 4 is a corrector step in the algorithm. In the algorithm, the predictor step decreases the dual gap as much as possible in a wider neighborhood of the central path and the corrector step draws iteration points back to a narrower neighborhood and make a reduction for the dual gap. It is shown that the algorithm has O(n~(1/2)L) iteration complexity which is the best result for convex quadratic programming so far.     

A linear programming-based optimization algorithm for solving nonlinear programming problems

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.     

Hybrid Flow-Shop: a Memetic Algorithm Using Constraint-Based Scheduling for Efficient Search

The paper considers the hybrid flow-shop scheduling problem with multiprocessor tasks. Motivated by the computational complexity of the problem, we propose a memetic algorithm for this problem in the paper. We first describe the implementation details of a genetic algorithm, which is used in the memetic algorithm. We then propose a constraint programming based branch-and-bound algorithm to be employed as the local search engine of the memetic algorithm. Next, we present the new memetic algorithm. We lastly explain the computational experiments carried out to evaluate the performance of three algorithms (genetic algorithm, constraint programming based branch-and-bound algorithm, and memetic algorithm) in terms of both the quality of the solutions produced and the efficiency. These results demonstrate that the memetic algorithm produces better quality solutions and that it is very efficient.     

求置换因子循环矩阵的逆阵及广义逆阵的快速算法

1 引 言 循环矩阵由于其应用非常广泛而成为一类重要的特殊矩阵,如在图象处理、编码理论、自回归滤波器设计等领域中经常会遇到以这类矩阵为系数的线性系统的求解问题.而对称循环组合系统也具有广泛的实际背景,例如造纸机的横向控制系统,具有平行结     

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Mehrotra’s algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra’s algorithm. This paper describes a proposal and implementation of an alternative algorithm, an arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by the arc-search infeasible interior-point algorithm and Mehrotra’s algorithm, that the proposed arc-search infeasible interior-point algorithm is a more reliable and efficient algorithm than Mehrotra’s algorithm.     

Finding feasible vectors of Edmonds-Giles polyhedra

A combinatorial algorithm for finding a feasible vector of the Edmonds-Giles polyhedron is presented. The algorithm is polynomially bounded provided that an oracle is available for minimizing submodular functions. A feasibility theorem is also proved by the algorithm and, as a consequence, a good algorithm for finding an integer-valued modular function between a sub- and a supermodular function is deduced. An important idea in the algorithm is due to Schönsleben and Lawler and Martel: the shortest augmenting paths have to be chosen in a lexicographic order.     

A comparison of sequential Delaunay triangulation algorithms

This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm.

Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.     

Approximate Simulation of Hawkes Processes

Hawkes processes are important in point process theory and its applications, and simulation of such processes are often needed for various statistical purposes. This article concerns a simulation algorithm for unmarked and marked Hawkes processes, exploiting that the process can be constructed as a Poisson cluster process. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work Møller and Rasmussen (2004). We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical results for the algorithm compared with perfect simulations. Extensions of the algorithm and the results to more general types of marked point processes are also discussed.     

A Newton Acceleration of the Weiszfeld Algorithm for Minimizing the Sum of Euclidean Distances

The Weiszfeld algorithm for continuous location problems can be considered as an iteratively reweighted least squares method. It generally exhibits linear convergence. In this paper, a Newton algorithm with similar simplicity is proposed to solve a continuous multifacility location problem with the Euclidean distance measure. Similar to the Weiszfeld algorithm, the main computation can be solving a weighted least squares problem at each iteration. A Cholesky factorization of a symmetric positive definite band matrix, typically with a small band width (e.g., a band width of two for a Euclidean location problem on a plane) is performed. This new algorithm can be regarded as a Newton acceleration to the Weiszfeld algorithm with fast global and local convergence. The simplicity and efficiency of the proposed algorithm makes it particularly suitable for large-scale Euclidean location problems and parallel implementation. Computational experience suggests that the proposed algorithm often performs well in the absence of the linear independence or strict complementarity assumption. In addition, the proposed algorithm is proven to be globally convergent under similar assumptions for the Weiszfeld algorithm. Although local convergence analysis is still under investigation, computation results suggest that it is typically superlinearly convergent.     

多目标规划的一种混合遗传算法

本文利用遗传算法的全局搜索内能力及直接搜索算法的局部优化能力，提出了一种用于多目标规划的混合遗传算法．与Pareto遗传算法相比．本文提出的算法能提高多目标遗传算法优化搜索效率，并保证了能得到适舍决策者要求的Pareto最优解．最后，理论与实践证明其有有效性．     

A simulated annealing driven multi-start algorithm for bound constrained global optimization

A derivative-free simulated annealing driven multi-start algorithm for continuous global optimization is presented. We first propose a trial point generation scheme in continuous simulated annealing which eliminates the need for the gradient-based trial point generation. We then suitably embed the multi-start procedure within the simulated annealing algorithm. We modify the derivative-free pattern search method and use it as the local search in the multi-start procedure. We study the convergence properties of the algorithm and test its performance on a set of 50 problems. Numerical results are presented which show the robustness of the algorithm. Numerical comparisons with a gradient-based simulated annealing algorithm and three population-based global optimization algorithms show that the new algorithm could offer a reasonable alternative to many currently available global optimization algorithms, specially for problems requiring ‘direct search’ type algorithm.