共查询到20条相似文献,搜索用时 500 毫秒
1.
In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming(LMP). The problem(LMP) is firstly converted into an equivalent programming problem(LMP(H))by introducing p auxiliary variables. Then by exploiting structure of(LMP(H)), a linear relaxation programming(LP(H)) of(LMP(H)) is obtained with a problem(LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems(LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm. 相似文献
2.
Cheng-xian Xu Xiao-liang Feng-min Xu 《计算数学(英文版)》2006,24(6):749-760
An effective continuous algorithm is proposed to find approximate solutions of NP-hardmax-cut problems.The algorithm relaxes the max-cut problem into a continuous nonlinearprogramming problem by replacing n discrete constraints in the original problem with onesingle continuous constraint.A feasible direction method is designed to solve the resultingnonlinear programming problem.The method employs only the gradient evaluations ofthe objective function,and no any matrix calculations and no line searches are required.This greatly reduces the calculation cost of the method,and is suitable for the solutionof large size max-cut problems.The convergence properties of the proposed method toKKT points of the nonlinear programming are analyzed.If the solution obtained by theproposed method is a global solution of the nonlinear programming problem,the solutionwill provide an upper bound on the max-cut value.Then an approximate solution to themax-cut problem is generated from the solution of the nonlinear programming and providesa lower bound on the max-cut value.Numerical experiments and comparisons on somemax-cut test problems(small and large size)show that the proposed algorithm is efficientto get the exact solutions for all small test problems and well satisfied solutions for mostof the large size test problems with less calculation costs. 相似文献
3.
The penalty function method, presented many years ago, is an important numerical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty function approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach. 相似文献
4.
倪勤 《高等学校计算数学学报(英文版)》2002,11(1):1-12
This paper represents an inexact sequential quadratic programming (SQP) algorithm which can solve nonlinear programming (NLP) problems. An inexact solution of the quadratic programming subproblem is determined by a projection and contraction method such that only matrix-vector product is required. Some truncated criteria are chosen such that the algorithm is suitable to large scale NLP problem. The global convergence of the algorithm is proved. 相似文献
5.
In this paper, a new trust region algorithm for nonlinear equality constrained LC^1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view. 相似文献
6.
LiPingZHANG JiYeHAN ZhengHaiHUANG 《数学学报(英文版)》2005,21(1):117-128
We propose a one-step smoothing Newton method for solving the non-linear complementarity problem with P0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function(for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0-NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions. 相似文献
7.
In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem. 相似文献
8.
Ju-liangZhang JianChen Xin-jianZhuo 《计算数学(英文版)》2004,22(4):509-522
In this paper, LCP is converted to an equivalent nonsmooth nonlinear equation system H(x,y) = 0 by using the famous NCP function-Fischer-Burmeister function. Note that some equations in H(x, y) = 0 are nonsmooth and nonlinear hence difficult to solve while the others are linear hence easy to solve. Then we further convert the nonlinear equation system H(x, y) = 0 to an optimization problem with linear equality constraints. After that we study the conditions under which the K-T points of the optimization problem are the solutions of the original LCP and propose a method to solve the optimization problem. In this algorithm, the search direction is obtained by solving a strict convex programming at each iterative point, However, our algorithm is essentially different from traditional SQP method. The global convergence of the method is proved under mild conditions. In addition, we can prove that the algorithm is convergent superlinearly under the conditions: M is P0 matrix and the limit point is a strict complementarity solution of LCP. Preliminary numerical experiments are reported with this method. 相似文献
9.
De Tong Zhu 《数学学报(英文版)》2008,24(12):2081-2100
We extend the classical affine scaling interior trust region algorithm for the linear constrained smooth minimization problem to the nonsmooth case where the gradient of objective function is only locally Lipschitzian. We propose and analyze a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the linear constrained LC1 optimization where the second-order derivative of the objective function is explicitly required to be locally Lipschitzian. The general trust region subproblem in the proposed algorithm is defined by minimizing an augmented affine scaling quadratic model which requires both first and second order information of the objective function subject only to an affine scaling ellipsoidal constraint in a null subspace of the augmented equality constraints. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions where twice smoothness of the objective function is not required. Applications of the algorithm to some nonsmooth optimization problems are discussed. 相似文献
10.
An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions. 相似文献
11.
In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial
fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic
difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear
underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently,
the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively
refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the
primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed
algorithm is feasible and can successfully be used to solve the present problem (P). 相似文献
12.
13.
14.
In this paper, a global optimization algorithm is proposed for solving sum of generalized polynomial ratios problem (P) which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solve the problem (P). For such problems, we present a branch and bound algorithm. In this method, by utilizing exponent transformation and new three-level linear relaxation method, a sequence of linear relaxation programming of the initial nonconvex programming problem (P) are derived which are embedded in a branch and bound algorithm. The proposed method need not introduce new variables and constraints and it is convergent to the global minimum of prime problem by means of the subsequent solutions of a series of linear programming problems. Several numerical examples in the literatures are tested to demonstrate that the proposed algorithm can systematically solve these examples to find the approximate ?-global optimum. 相似文献
15.
为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的. 相似文献
16.
17.
本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的. 相似文献
18.
19.
Harold P. Benson 《Journal of Global Optimization》2002,22(1-4):343-364
This article presents a branch and bound algorithm for globally solving the nonlinear sum of ratios problem (P). The algorithm works by globally solving a sum of ratios problem that is equivalent to problem (P). In the algorithm, upper bounds are computed by maximizing concave envelopes of a sum of ratios function over intersections of the feasible region of the equivalent problem with rectangular sets. The rectangular sets are systematically subdivided as the branch and bound search proceeds. Two versions of the algorithm, with convergence results, are presented. Computational advantages of these algorithms are indicated, and some computational results are given that were obtained by globally solving some sample problems with one of these algorithms. 相似文献
20.
This paper presents an efficient branch and bound algorithm for globally solving sum of geometric fractional functions under geometric constraints, which arise in various practical problems. By using an equivalent transformation and a new linear relaxation technique, a linear relaxation programming problem of the equivalent problem is obtained. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems. Numerical results are reported to show the feasibility of our algorithm. 相似文献