区间规划问题的最优性条件

运筹与管理 ›› 2014, Vol. 23 ›› Issue (1): 39-43.

区间规划问题的最优性条件

孙玉华¹, 许平¹, 王来生²

1.北京科技大学数理学院,北京 100083;
2.中国农业大学理学院,北京 100083

收稿日期:2012-03-02 出版日期:2014-01-25
作者简介:孙玉华,女,博士,副教授;王来生,男,博士,教授。
基金资助:
国家自然科学基金资助项目(11271367)

Optimality Conditions for Interval-Valued Programming

SUN Yu-hua^1,2, XU Ping¹, WANG Lai-sheng²

1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
2. College of Science, China Agricultural University, Beijing 100083, China

Received:2012-03-02 Online:2014-01-25

摘要/Abstract

摘要： 区间规划是带有区间参数的规划问题,是一种更易于求解实际问题的柔性规划。它是确定性优化问题的延伸,有区间线性规划和区间非线性规划两种形式。本文讨论了目标函数是区间函数的区间非线性问题。给出了区间规划问题最优性必要条件的较简单证明方法,并利用LU最优解的概念,在一类广义凸函数－(p,r)－ρ－(η,θ)－不变凸函数定义下讨论了最优性充分条件。

关键词: 不确定优化, 区间规划, 最优性条件, (p,r)－ρ－(η,θ)－不变凸函数。

Abstract: The programming with interval coefficients is called interval programming, which is flexible programming to easily solve some optimization problems. Interval programming can be regarded as an extension of deterministic optimization problems. There are two kinds of interval programming: interval linear programming and interval nonlinear programming. In this paper, we discuss interval-valued programming where the objective function is an interval-valued function. The necessary optimality conditions are established for a feasible point to LU optimal solution, and the sufficient optimality conditions are obtained under(p,r)－ρ－(η,θ)－ invexity assumptions on objective and the constraint functions.

Key words: uncertain optimization, interval-valued programming, optimality conditions, (p,r)－ρ－(η,θ)－invexity functions.

中图分类号:

O224
O221.2

孙玉华, 许平, 王来生. 区间规划问题的最优性条件[J]. 运筹与管理, 2014, 23(1): 39-43.

SUN Yu-hua, XU Ping, WANG Lai-sheng. Optimality Conditions for Interval-Valued Programming[J]. Operations Research and Management Science, 2014, 23(1): 39-43.

参考文献

[1] Ishibuchi H, Tanaka H. Multiobjective programming in optimization of the interval objective function[J]. Eur. J. Oper. Res., 1990, 48: 219-225.
[2] Tong S C. Interval number and fuzzy number linear programming[J]. Fuzzy Sets Syst., 1994, 66: 301-306.
[3] Ida M. Portfolio selection problem with interval coefficients[J]. Appl. Math. Lett., 2003, 16: 709-713.
[4] Huang Y F, Baetz B W, Huang G H. Violation analysis for solid waste management systems: an interval fuzzy programming approach[J]. J. Environ. Manage., 2002, 65: 431-446.
[5] Oliveira C. Multiple objective linear programming models with interval coefficients-illustrated overview[J]. Eur. J. Oper. Res., 2007, 181: 1434-1463.
[6] Alefeld G, Mayer G. Interval analysis: theory and applications[J]. J. Comput. Appl. Math., 2000, 121: 421-464.
[7] Ding K, Huang N J. A new class of interval projection neural networks for solving interval quadratic program[J]. Chaos Solitons Fract., 2008, 25: 718-725.
[8] Li W, Tian X L. Numerical solution method for general interval quadratic programming[J]. Appl. Math. Comput., 2008, 202: 589-595.
[9] Wu H C. Duality theory for optimization problems with interval-valued objective functions[J]. J. Optim. Theory Appl., 2010, 144: 615-628.
[10] Wu H C. Wolfe duality for interval-valued optimization[J]. J. Optim. Theory Appl., 2008, 138: 497-509.
[11] Wu H C. On interval-valued nonlinear programming problems[J]. J. Math. Anal. Appl., 2008, 338: 299-316.
[12] Zhou H C, Wang Y J. Optimality condition and mixed duality for interval-valued optimization[J].Fuzzy Info. and Eng., AISC, 2009, 62: 1315-1323.
[13] Sun Y H, Wang L S. Saddle-point type optimality for interval-valued programming[C].Proc. Int. Conf. Uncertainty Reasoning Knowl. Eng., URKE, 2012, 8: 252-255.
[14] Mandal P, Nahak C. Symmetric duality with(p,r)－ρ－(η,θ)-invexity[J]. Appl. Math. Comput., 2011, 217: 8141-8148.
[15] Bazaraa M S, Sherali H D, Shetty C M. Nonlinear programming: Theory and algorithms[M]. Third Edition. New York: Wiley-Interscience, 2006.