一种求解混合非线性整数规划的支撑超平面方法

被引：4

作者：

达林

查建中

机构：

[1] 北京交通大学机械与电子控制工程学院

来源：

系统工程理论与实践 | 2008年 / 09期

关键词：

凸规划; 扩展切平面(ECP); 支撑超平面(SHP); 混合整数非线性规划(MINLP);

D O I：

暂无

中图分类号：

O221.4 [整数规划];

学科分类号：

摘要：

给出一种在可行域边界生成支撑超平面(Supporting Hyper Plane,SHP)的方法来求解凸混合整数非线性(Mixed Integer Nonlinear Programming,MINLP)问题.扩展切平面(Extended Cutting Plane,ECP)算法作为求解混合整数非线性规划的一种重要方法,在算法结构上简单,鲁棒性强,但是该算法收敛速度慢,特别是当被求解问题非线性程度比较高时.SHP算法在每次迭代过程中对可行域的估计比ECP算法更准确(更小),从而加快了算法的收敛速度.和ECP方法相比,SHP算法有效的提高了求解MINLP问题的效率,数值试验显示了该方法的有效性.

引用

页码：82 / 86+111 +111

页数：6

共 10 条

[1]

An extended cutting plane method for solving convex MINLP problems[J] . Tapio Westerlund,Frank Pettersson.Computers and Chemical Engineering . 1995

[2] BRANCH AND BOUND EXPERIMENTS IN CONVEX NONLINEAR INTEGER PROGRAMMING [J].

GUPTA, OK ;

RAVINDRAN, A .

MANAGEMENT SCIENCE, 1985, 31 (12) :1533-1546

[3]

pth Power Lagrangian Method for Integer Programming[J] . Duan Li,Douglas J. White.Annals of Operations Research . 2000 (1)

[4]

Trivial integer programs unsolvable by branch-and-bound[J] . R. G. Jeroslow.Mathematical Programming . 1974 (1)

[5] AN OUTER-APPROXIMATION ALGORITHM FOR A CLASS OF MIXED-INTEGER NONLINEAR PROGRAMS [J].

DURAN, MA ;

GROSSMANN, IE .

MATHEMATICAL PROGRAMMING, 1986, 36 (03) :307-339

[6]

Solving mixed integer nonlinear programs by outer approximation[J] . Roger Fletcher,Sven Leyffer.Mathematical Programming . 1994 (1)

[7] Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques [J].

Grossmann, Ignacio E. .

OPTIMIZATION AND ENGINEERING, 2002, 3 (03) :227-252

[8] Integrating SQP and branch-and-bound for mixed integer nonlinear programming [J].

Leyffer, S .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2001, 18 (03) :295-309

[9]

Generalized Benders decomposition[J] . A. M. Geoffrion.Journal of Optimization Theory and Applications . 1972 (4)

[10]

Mixed discrete constrained nonlinear programming via recursive quadratic programming. Cha J Z. State University of New York atBuffalo . 1987

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