OPTIMAL GEOMETRIC PROCESS REPLACEMENT MODEL

In this paper, we study the geometric process replacement model as follows:the successivesurvival times of the system form a nonincreasing geometric process while the consecutive repairtimes of the system constitute a non-decreasing geometric process, and the system is replacedat the time of the Nth failure after its installation or last replacement. Based on the long-runaverage cost per unit time, we determine the optimal replacement policy N,show the uniquenessof the policy N and discuss its monotonicity.     

DETERMINATION OF PERMANENT OPTIMAL DATA POINTS AND AN EFFICIENT ALGORITHM FOR LAD PROBLEM

This paper gives a definition of permanent optimal data point of Least Absolute Deviation(LAD)problem.Some theoretical results on non-degenerate LAD problem are obtained.For computing LAD problem,an efficient,algorithm is given according to the idea of permanent optimal data point.Numerical experience shows that our algorithm is better than many of others,including the famous B R 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 ALGORITHM FOR DECOMPOSING ZERO-DIMENSIONAL POLYNOMIAL IDEALS

本文给出了一种不使用线性变换和ｖ．ｄ．Ｗａｅｒｄｅｎ的指数方法的零维多项式理想准素分解的新方法     

AN INTERVAL ALGORITHM FOR CONSTRAINED GLOBAL OPTIMIZATION

In order to solve the constrained global optimization problem,we use penalty functions not only on constraints but also on objective function. Then within the framework of interval analysis,an interval Branch-and-Bound algorithm is given,which does not need to solve a sequence of unconstrained problems. Global convergence is proved. Numerical examples show that this algorithm is efficient.     

A COMBINED ALGORITHM FOR IDENTIFICATION AND APPROXIMATION

The optimum point of an unknown function which is measured with noise and the unknownparameters in the measurment noise are estimated by a combined algorithm.The almost sure conver-gence and the convergence rate are established for both unconstrained and constrained problems.     

OPTIMAL PREDICTION FOR LINEAR DISCRETE-TIME DISTRIBUTED PARAMETER SYSTEMS

In this paper we deal with the optimal predicated problem for distributed parameter system-state of Gauss-Markov, which can be described by vector difference integral equations. When the optimal filtered estimate and covariance matrix are known the optimal preredicated formula and the covariance matrix equation of the system state are derived, moreover we have shown that the obtained predicated error process is also a Gauss-Markov distributed parameter process. We have shown that the optimal recursive filtered estimate formula and equations for error covariance can be derived by projection lemma.     

AN OUTER APPROXIMATION ALGORITHM FOR SEMI-INFINITE NONDIFFERENTIABLE PROGRAMMINGS

This paper presents a conceptual outer approximation algorithm for dealing with the semi-infinite nondifferentiable programming in which functions are locally Lipschitzian. By weakening the restriction on the family of functions for a parametric programming, we answer a question proposed in [1].     

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

The simplified Newton method, at the expense of fast convergence, reduces the work required by Newton method by reusing the initial Jacobian matrix. The composite Newton method attempts to balance the trade-off between expense and fast convergence by composing one Newton step with one simplified Newton step. Recently, Mehrotra suggested a predictor-corrector variant of primal-dual interior point method for linear programming. It is currently the interior-point method of the choice for linear programming. In this work we propose a predictor-corrector interior-point algorithm for convex quadratic programming. It is proved that the algorithm is equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require that the initial primal and dual points be feasible. Numerical experiments are made.     

AN ALGORITHM FOR SOLVING SYSTEM OF LINEAR INEQUALITIES

A new algorithm is presented for solving a system of linear inequalities. Starting at any point by solving a least squares problem we can either obtain a feasible point or determine that no solution exists.     

THE CONVERGENCE OF GLOWINSKI'S ALGORITHM FOR ELLIPTIC PROBLEMS

ＴＨＥＣＯＮＶＥＲＧＥＮＣＥＯＦＧＬＯＷＩＮＳＫＩ＇ＳＡＬＧＯＲＩＴＨＭＦＯＲＥＬＬＩＰＴＩＣＰＲＯＢＬＥＭＳＣＨＵＤＥＬＩＮ（储德林）；ＨＵＸＩＡＮＣＨＥＮＧ（胡显承）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇ－Ｈｕ...     

PROXIMAL POINT ALGORITHM FOR MINIMIZATION OF DC FUNCTION

In this paper we present some algorithms for minimization of DC function (difference of two convex functions). They are descent methods of the proximal-type which use the convex properties of the two convex functions separately. We also consider an approximate proximal point algorithm. Some properties of the ε-subdifferentiM and the ε-directional derivative are discussed. The convergence properties of the algorithms are established in both exact and approximate forms. Finally, we give some applications to the concave programming and maximum eigenvalue problems.     

AN EFFICIENT P-D ALGORITHM FOR SHORTEST PATH PROBLEM

ThisresearchissupportedbytheNationalNaturalScienceFoundationofChinaunderGrant19271023.Therearenumerousproblemsincombinatorialoptimization.Theirsolutionsaredifferentfromoneanother.Ithasnotbeenfoundanunifiedapproachthatcanbeusedtoailproblemsincombinatorialoptimization.However,therestillexistsanunifiedapproachthatcanbeusedtosolveaclassofproblemsincombinatorialoptimizationrelatingtographs,thisapproachisprimal-dualalgorithm.(WesimplycallPDalgorithm).Inlinearprogram,wesolveDRPtogetanoptimalsol…     

A NEW ALGORITHM FOR BALL-CONSTRAINED QUADRATIC MINIMIZATION PROBLEMS

A new algorithm for the ball-constrained quadratic minimization problem min ,with a symmetric semi-positive definite matrix H and nonzero vector 6 , is presented:zk+1 > 0, k= 0,1,2,…,where z0 > 0 , and S, = Si(zk) = bT(H + zkl)-ib, i = 2,3,4.We proved that, the iterative sequence converges monotonically to the unique minimum norm minimizer x:And the convergence rate of is 3,2, and 4/3 according to z > 0, lim S2(z) < 1 and lim S2(z)= 1 respectively.     

A NONMOTOTONE ALGORITHM FOR MINIMIZING NONSMOOTH COMPOSITE FUNCTIONS

In this paper, we present a nonmonotone algorithm for solving nonsmooth composite optimization problems. The objective function of these problems is composited by a nonsmooth convex function and a differentiable function. The method generates the search directions by solving quadratic programming successively, and makes use of the nonmonotone line search instead of the usual Armijo-type line search. Global convergence is proved under standard assumptions. Numerical results are given.     

A MINIMIZING ALGORITHM FOR COMPLEX NONCONVEX NONDIFFERENTIABLE FUNCTIONS

The minimization of nonconvex, nondifferentiable functions that are compositions of max-type functions formed by nondifferentiable convex functions is discussed in this paper. It is closely related to practical engineering problems. By utilizing the globality of ε-subdifferential and the theory of quasidifferential, and by introducing a new scheme which selects several search directions and consider them simultaneously at each iteration, a minimizing algorithm is derived. It is simple in structure, implementable, numerically efficient and has global convergence. The shortcomings of the existing algorithms are thus overcome both in theory and in application.     

LEVERRIER-LAGUERRE ALGORITHM FOR THE MATRIX POLYNOMIAL OF DEGREE TWO

1　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＡｂｅａｎ×ｎｍａｔｒｉｘ ,Ｉｎｄｅｎｏｔｅｓｔｈｅｕｎｉｔｍａｔｒｉｘｏｆｏｒｄｅｒｎ .Ａｎｄｌｅｔ ａ(λ) =ｄｅｔ(λＩｎ-Ａ) =λｎ+ ａ1λｎ- 1+… + ａｎ- 1λ+ ａｎ (1 .1 )ｂｅｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｐｏｌｙｎｏｍｉａｌｏｆＡ ,ｔｈｅａｄｊｏｉｎｔｍａｔｒｉｘｏｆλＩｎ-Ａｂｅ Ｂ(λ) =ａｄｊ(λＩｎ-Ａ) =λｎ- 1Ｉｎ+λｎ- 2 Ｂ1+… +λ Ｂｎ- 2 + Ｂｎ- 1. (1 .2 )Ｔｈｅｎ(λΙｎ-Ａ) - 1= Ｂ(λ) / ａ(λ) . (1 .3)　　Ａｗｅｌｌ ｋｎｏｗＬｅｖｅｒｒｉ…     

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.