A QR DECOMPOSITION BASED SOLVER FOR THE LEAST SQUARES PROBLEMS FROM THE MINIMAL RESIDUAL METHOD FOR THE SYLVESTER EQUATION

Based on the generalized minimal residual （GMRES） principle, Hu and Reichel proposed a minimal residual algorithm for the Sylvester equation. The algorithm requires the solution of a structured least squares problem. They form the normal equations of the least squares problem and then solve it by a direct solver, so it is susceptible to instability. In this paper, by exploiting the special structure of the least squares problem and working on the problem directly, a numerically stable QR decomposition based algorithm is presented for the problem. The new algorithm is more stable than the normal equations algorithm of Hu and Reichel. Numerical experiments are reported to confirm the superior stability of the new algorithm.     

Joint optimization traffic signal control for an urban arterial road

This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.     

一类无约束离散Minimax问题的区间调节熵算法

In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C^1. The paper deals with this problem by means of taking the place of maximum-entropy function with adjustable entropy function. By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented. The relevant properties are proven, The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum-entropy algorithm. Both theoretical and numerical results show that the method is reliable and efficient.     

Pendants-median支撑树及其一个相关问题:复杂性和算法

The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3).     

A Robust Algorithm for Blind Total Variation Restoration

Image restoration is a fundamental problem in image processing. Blind image restoration has a great value in its practical application. However, it is not an easy problem to solve due to its complexity and difficulty. In this paper, we combine our robust algorithm for known blur operator with an alternating minimization implicit iterative scheme to deal with blind deconvolution problem, recover the image and identify the point spread function（PSF）. The only assumption needed is satisfy the practical physical sense. Numerical experiments demonstrate that this minimization algorithm is efficient and robust over a wide range of PSF and have almost the same results compared with known PSF algorithm.     

广义几何规划的压缩共轭梯度路径非单调信赖域算法(英文)

In this paper,on the basis of making full use of the characteristics of unconstrained generalized geometric programming（GGP）,we establish a nonmonotonic trust region algorithm via the conjugate path for solving unconstrained GGP problem.A new type of condensation problem is presented,then a particular conjugate path is constructed for the problem,along which we get the approximate solution of the problem by nonmonotonic trust region algorithm,and further prove that the algorithm has global convergence and quadratic convergence properties.     

A new algorithm for pole assignment of single-input linear systems using state feedback

In this paper we present a new algorithm for the single-input pole assignment problem using state feedback. This algorithm is based on the Schur decomposition of the closed-loop system matrix, and the numerically stable unitary transformations are used whenever possible, and hence it is numerically reliable.The good numerical behavior of this algorithm is also illustrated by numerical examples.     

GAUSSIAN PIVOTING METHOD FORSOLVING LINEAR COMPLEMENTARITY PROBLEM

In this paper, a new direct algorithm for solving linear complementarity problem with Z-matrix is proposed. The algorithm exhibits either a solution or its nonexistence after at most n steps (where n is the dimension of the problem) and the computational complexity is at most 1/3n^2 O(n^2)     

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （Part Ⅱ Heuristics for the General Case）

A single machine scheduling problem with controllable processing times and compression costs is considered. The objective is to find an optimal sequence to minimize the cost ofcompletion times and the cost of compression. The complexity of this problem is still unknown.In Part Ⅱ of this paper,the authors have considered a special case where the compression timesand the compression costs are equal among all jobs. Such a problem appears polynomiafiy solvable by developing an O(n^2) algorithm. In this part(Part Ⅱ ),a general case where the controllable processing times and the compression costs are not equal is discussed. Authors proposehere two heuristics with the first based on some previous work and the second based on the algorithm developed in Part Ⅱ . Computational results are presented to show the efficiency and therobustness of these heuristics.     

Optimal Control Problem Governed by Semilinear Parabolic Equation and its Algorithm

In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified.     

A SQP METHOD FOR GENERAL NONLINEAR COMPLEMENTARITY PROBLEMS

§ 1　 IntroductionThe nonlinear complementarity problem(NCP) is to find a pointx∈Rn such thatx Tf(x) =0 ,x≥ 0 ,f(x)≥ 0 ,(1 .1 )where f is a continuously differentiable function from Rninto itself.It is well known thatthe NCP is equivalent to a system of smoothly nonlinear equations with nonnegative con-straintsH (z)∶ =y -f(x)x . y =0 ,s.t. x≥ 0 ,y≥ 0 ,(1 .2 )where z=(x,y) and x y=(x1 y1 ,...,xnyn) T.Based on the above reformulation,many in-terior-point methods are established;see,fo…     

解P_0非线性互补问题的光滑Levenberg-Marquardt方法

本文研究了一个P0非线性互补问题.利用信赖域技术获得了求解该问题的光滑Levenberg-Marquardt算法,该算法在一定条件下具有全局性.利用局部误差界还获得了该算法的超线性和二次收敛.数值结果表明该算法是有效的.     

Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations

We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs.This research was supported by the Singapore-MIT Alliance and the Australian Research Council.     

A smoothing-type algorithm for solving system of inequalities

In this paper we consider system of inequalities. By constructing a new smoothing function, the problem is approximated via a family of parameterized smooth equations. A Newton-type algorithm is applied to solve iteratively the smooth equations so that a solution of the problem concerned is found. We show that the algorithm is globally and locally quadratically convergent under suitable assumptions. Preliminary numerical results are reported.     

An Algorithm for Continuous Type Optimal Location Problem

In this paper, we extend the ordinary discrete type facility location problems to continuous type ones. Unlike the discrete type facility location problem in which the objective function isn't everywhere differentiable, the objective function in the continuous type facility location problem is strictly convex and continuously differentiable. An algorithm without line search for solving the continuous type facility location problems is proposed and its global convergence, linear convergence rate is proved. Numerical experiments illustrate that the algorithm suggested in this paper have smaller amount of computation, quicker convergence rate than the gradient method and conjugate direction method in some sense.     

Armijo线性搜索下的多步下降算法

本文研究无约束优化问题.利用前面多步迭代点的信息产生下降方向以及Armijo线性搜索产生步长,得到了一类新的多步下降算法,并且在较弱条件下证明了算法具有全局收敛性和线性收敛速率.初步的数值试验表明算法是有效的.     

A NEW SMOOTHING EQUATIONS APPROACH TO THE NONLINEAR COMPLEMENTARITY PROBLEMS

The nonlinear complementarity problem can be reformulated as a nonsmooth equation. In this paper we propose a new smoothing Newton algorithm for the solution of the nonlinear complementarity problem by constructing a new smoothing approximation function. Global and local superlinear convergence results of the algorithm are obtained under suitable conditions. Numerical experiments confirm the good theoretical properties of the algorithm.     

On the convergence of a modified algorithm for the spherical facility location problem

We study the spherical facility location problem which is a more realistic model than the Euclidean facilities location. We present a modified algorithm for this problem, which has the following good properties: (a) It is very easy to initialize the algorithm with an arbitrary point as its starting point; (b) Under suitable assumptions, it is proved that the algorithm globally converges to a global minimizer of the problem.     

General Information

In this paper, a new sequential penalty algorithm, based on the L_infin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm.     

关于求解变分不等式问题的2-次梯度外梯度算法收敛性的一个补注

Yair Censor,Aviv Gibali和Simeon Reich为求解变分不等式问题提出了 2-次梯度外梯度算法.关于此算法的收敛性,作者给出了部分证明,有一个问题:由算法产生的迭代点列能否收敛到变分不等式问题的一个解上,没有得到解决.此问题作为一个公开问题在文章"Extensions of Korpelevi...