English

运筹学学报 >

2017 , Vol. 21 >Issue 1: 33 - 43

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2017.01.004

运筹学

等式约束优化问题的一类新的简单光滑精确罚函数

展开
  • 1. 曲阜师范大学管理学院, 山东日照  276826  

收稿日期: 2016-02-01

  网络出版日期: 2017-03-15

基金资助

国家自然科学基金(Nos. 71371107, 61373027), 山东省自然科学基金(No. ZR2013AM013)

收起

 A new class of simple smooth exact penalty functions  for equality constrained optimization problems

Expand
  • 1. School of Management, Qufu Normal University, Rizhao 276826, Shandong, China

Received date: 2016-02-01

  Online published: 2017-03-15

Fold

摘要

LIAN Shujun,  DU Aihua,  TANG Jiahui

关键词： 非线性规划; 约束最优化; 精确罚函数; 光滑罚函数

本文引用格式

连淑君, 杜爱华, 唐加会 . 等式约束优化问题的一类新的简单光滑精确罚函数[J]. 运筹学学报, 2017 , 21(1) : 33 -43 . DOI: 10.15960/j.cnki.issn.1007-6093.2017.01.004

Abstract

Exact penalty function method is one of the main approaches for solving constrained nonlinear programming problems. For the traditional exact penalty function,  it is not both smooth and simple. It is simple in the sense that the gradient of the objective function and constrained functions is not involved in the penalty function. In this paper, a new class of simple and smooth penalty functions which are different from the tradition penalty functions is proposed for the equality constrained problem. It is proved that the class of exact penalty functions is exact. The algorithm based on the new smoothed penalty functions is proposed. Two numerical examples show that the algorithm is efficient.

Key words： nonlinear programming; constrained optimization; exact penalty function; smooth penalty function

参考文献

[1]  Cominetti R, Dussault J P. Stable exponential-penalty algorithm with superlinear convergence [J]. Journal of Optimization Theory and Applications, 1994, 83(2): 285-309.
[2] Conn A R, Gould N I M, Toint Ph L. Methods for nonlinear constraints in optimization calculation [M]//The State of the Art in Numerical Analysis. Oxford: Clarendon Press, 1997, 363-390.
[3] Fletcher R. Penalty functions [M]//Mathematical Programming, Berlin Heidelberg: Springer-Verlag, 1983, 87-114.
[4] Lucidi S. New results on a continuously differentiable exact penalty function [J]. SIAM Journal on Optimization, 1992, 2(4): 558-574.
[5] Pillo G D, Groppo L. A continuously differentiable exact penalty function [J]. SIAM Journal on Control and Optimization, 1985, 23(1): 72-84.
[6]  Pillo G D, Groppo L. An exact penalty method with global convergence properties for nonlinear programming problems [J]. Mathematical Programming, 1986, 36: 1-18.
[7]  Pillo G D. Exact penalty methods [M]//Algorithms for Continuous Optimization, Netherlands: Kluwer Academic Publishers, 1994, 209-253.
[8] Shanno D F, Simantiraki E M. Interior point methods for linear and nonlinear programming [M]//The State of the Art in Numerical Analysis, Oxford: Clarendon Press, 1997, 339-362.
[9] Tseng P, Bertsekas D P. On the convergence of the exponential multiplier method for convex programming [J]. Mathematical Programming, 1993, 60: 1-19.
[10]  尚有林, 刘牧华, 李璞. 一种新的逼近精确罚函数的罚函数及性质 [J]. 运筹学学报, 2012, 16(1): 56-66.
[11] Yu C, Teo K L, Bai Y. An exact penalty function method for nonlinear mixed discrete programming Problems [J]. Optimization Letters, 2013, 7(1): 23-38.
[12] 王长钰, 赵文玲. 约束优化问题的一类光滑罚算法的全局收敛特性 [J]. 运筹学学报, 2015, 19(3): 151-160.
[13] Ma C, Zhang L S. On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems [J]. Applied Mathematics and Computation, 2015, 271: 642-656.
[14] Huyer W, Neumaier A. A new exact penalty function [J]. SIAM Journal on Optimization, 2003, 13(4): 1141-1158.
[15] Lian S J, Zhang L S. A simple smooth exact penalty function for smooth optimization problems [J]. Journal of Systems Science \& Complexity, 2012, 25(3): 521-528.
[16] Mangasarian O L, Fromovitz S. The Fritz John necessary optimality conditions in the presence of equality and inequality constraints [J]. Journal of Mathematical Analysis and Applications, 1967, 17: 37-47.
Options
文章导航

/

〈 〉