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A new trust-region algorithm for solving a constrained optimization problem is introduced. In this algorithm, an active set strategy is used together with multiplier method to convert the computation of the trial step to easy trust-region subproblem similar to this for the unconstrained case. A convergence theory for this algorithm is presented. Under reasonable assumptions, it is shown that the algorithm is globally convergent. In particular, it is shown that, in the limit, a subsequence of the iteration sequence satisfies one of four types of stationary conditions. Namely, the infeasible Mayer–Bliss conditions, Fritz John’s conditions, the infeasible Fritz John’s conditions or KKT conditions. Preliminary numerical experiment on the algorithm is presented. The performance of the algorithm is reported. The numerical results show that our approach is of value and merit further investigation.

This paper presents a compensated algorithm to accurately evaluate a polynomial expressed in Chebyshev basis of the first and second kind with floating-point coefficients. The principle is to apply error-free transformations to improve the traditional Clenshaw algorithm. The new algorithm is as accurate as the Clenshaw algorithm performed in twice the working precision. Forward error analysis and numerical experiments illustrate the accuracy and properties of the proposed algorithm.

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].

A Gaussian kernel approximation algorithm for a feedforward neural network is presented. The approach used by the algorithm, which is based on a constructive learning algorithm, is to create the hidden units directly so that automatic design of the architecture of neural networks can be carried out. The algorithm is defined using the linear summation of input patterns and their randomized input weights. Hidden-layer nodes are defined so as to partition the input space into homogeneous regions, where each region contains patterns belonging to the same class. The largest region is used to define the center of the corresponding Gaussian hidden nodes. The algorithm is tested on three benchmark data sets of different dimensionality and sample sizes to compare the approach presented here with other algorithms. Real medical diagnoses and a biological classification of mushrooms are used to illustrate the performance of the algorithm. These results confirm the effectiveness of the proposed algorithm.

In this paper, a new descent algorithm for solving unconstrained optimization problem is presented. Its search direction is descent and line search procedure can be avoided except for the first iteration. It is globally convergent under mild conditions. The search direction of the new algorithm is generalized and convergence of corresponding algorithm is also proved. Numerical results show that the algorithm is efficient for given test problems.

The optimal fractional system identification is a challenging problem as it requires the estimation of not only the numerator parameters, but also the poles transfer function model and the non-integer order reading to complex nonlinear optimization. In this paper, an algorithm using the least square method, called “Vector Fitting” (V.F.) developed by Gustavsen is extended to the fractional order system identification in frequency domain. This algorithm proceeds recursively contrarily to the well known Levy’s algorithm which uses only one iteration to calculate the model parameters. The use of an iterative method efficiently directs the model parameters evolution towards their optimal values. Indeed, during iteration the poles of the model are calculated and used as starting poles for the next one, the stability of the identified model can thus be imposed. The V.F. algorithm is then associated with the heuristic optimization method: particle swarm optimization (PSO), leading to a new fractional system identification algorithm. The algorithm works in a hierarchical way; in a higher level, PSO determines the non-integer order and in a lower stage, the V.F. algorithm identifies the other parameters.

Perspective-five-point (P5P) problem is a classical problem in applied mathematics, pattern recognition and computer vision. We briefly survey several existing algorithms for the problem, and present a new linear algorithm (CSNM algorithm) to solve the P5P problem, which is based on a symbolic-numeric method from the geometric theory of partial differential equations. The proposed algorithm is stable robust. In particular, it can deal with the points near critical configurations. Numerical experiments are given to show the performance of our novel algorithm. (C) 2008 Elsevier Inc. All rights reserved.

This article presents a duality-bounds algorithm for globally solving a non-convex quadratic programming problem (P) that contains several additional multiterm multiplicative constraints. To our knowledge, little progress has been made so far for globally solving (P). The algorithm uses a branch-and-bound scheme where Lagrange duality theory is used to obtain the lower bounds. As a result, the lower bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently. Convergence of the algorithm is proved and a solved sample problem is given to show the feasibility of the proposed algorithm.

In this paper, based on combined homotopy interior point method we propose an interior point algorithm for convex nonlinear programming. The algorithm ensures that the obtained iterative points are interior points of the feasible set in terms of the technique of β-cone neighborhood. We establish the global convergence of the algorithm. Furthermore, it is shown that the algorithm has O ( n L ) iteration complexity. The preliminary numerical experiments indicate that the algorithm is efficient.

In this paper we present a study of the computational cost of the GNG3D algorithm for mesh optimization. This algorithm has been implemented taking as a basis a new method which is based on neural networks and consists on two differentiated phases: an optimization phase and a reconstruction phase. The optimization phase is developed applying an optimization algorithm based on the Growing Neural Gas model, which constitutes an unsupervised incremental clustering algorithm. The primary goal of this phase is to obtain a simplified set of vertices representing the best approximation of the original 3D object. In the reconstruction phase we use the information provided by the optimization algorithm to reconstruct the faces thus obtaining the optimized mesh. The computational cost of both phases is calculated, showing some examples.

An approximation algorithm for solving a sort of non-smooth programming is proposed. In the programming, the objective function is the Holder function and the feasible region is contained in a rectangle (viz. hyper-rectangle). To establish the algorithm, the properties of the Holder function and an approximation of the function by using Bernstein α-polynomial are studied. According to the properties of the approximation polynomial and the algorithm for solving geometric programming, the strategy for branching and bounding and the branch-and-bound algorithm are constructed to solve the programming. The convergence of the algorithm can be guaranteed by the exhaustive of the bisection of the rectangle. The feasibility of the algorithm is validated by solving an example.

The work presented in this paper focuses on parallel iterative algorithm for solving band linear systems. With suitable decomposition of coefficient matrix and using the form of the iterative formula of the BSOR serial method, a parallel algorithm on distributed-memory multi-computer is established. Then Eq. (7) , (8) are provided for carrying out computation required by our parallel algorithm. Furthermore, convergence is proved when the coefficient matrix A is Hermite positive definite matrix or M-matrix, and the sufficient condition is given. According to theoretical analysis, this algorithm has the same convergent velocity as BSOR method, and has the same parallelism as BJ method. In the end, two illustrative examples implemented on HP rx2600 cluster show that our algorithm’s parallel acceleration rates and efficiency are higher.

This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the algorithm only requires the second-order moments of the signal and the white noise perturbing its observations. Practical application of the proposed algorithm is illustrated with a restoration image problem.

In this paper, a parallel algorithm for solving block-tridiagonal linear systems on distributed-memory multi-computer is presented. According to theoretical analysis, convergent velocity and complexity of this algorithm are the same as BSOR method's, and parallelism is the same as BJ method's. Moreover, two examples have been implemented on HP rx2600 cluster, and the numerical experiments indicate that our algorithm is feasible and effective.

In the paper we present a new descent algorithm with curve search rule for unconstrained minimization problems. At each iteration, the next iterative point is determined by means of a curve search rule. It is particular that the search direction and the step-size is determined simultaneously at each iteration of the new algorithm. The algorithm, similarly to conjugate gradient methods, avoids the computation and storage of some matrices associated with the Hessian of objective functions. Unlike ODE methods, it is not required to solve ordinary differential equations at each iteration. Although the convergence rate of our algorithm is not as fast as that of Newton-like methods, it is suitable to solve large scale minimization problems.

A Leverrier-like algorithm is presented which allows the computation of the transfer function of a linear regular system from its 2-D state-space description, without inverting a multivariable polynomial matrix. This algorithm is an extension of the classic Leverrier's algorithm for 1-D system and it reduces the computational cost. 2-D Cayley-Hamilton theorem is also shown by the algorithm.

A new trust-region active-set algorithm for solving minimizing a nonlinear function subject to nonlinear equality and inequality constraints is described. In this algorithm, an active set strategy is used together with a projected Hessian technique to compute the trial step. A convergence theory for this algorithm is presented. Under important assumptions, it is shown that the algorithm is globally convergent. In particular, it is shown that a subsequence of the iteration sequence is not bounded away from either Fritz-John points or KKT points.

This paper presents a finite algorithm for computing the weighted Moore-Penrose inverse of a rectangular matrix. This algorithm may be viewed as an extension of Decell's algorithm.