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一类等式约束非线性优化问题的信赖域新算法 被引量：1

A Trust-region Method for Nonlinear Optimization with Equations Constrained
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摘要 提出一类信赖域新算法用于求解等式约束的非线性优化问题,在构造增广拉格朗日函数的基础上,提出了信赖域子问题的求解公式,研究了拉格朗日乘子和罚因子的修正公式,并使用滤子技巧,放松了接受尝试步的条件,证明了算法的收敛性.最后进行了数值试验. This paper proposes a new class of trust region algorithm for solving equality constrained nonlinear optimization problems.The trust region subproblem formula is presented based on augmented Lagrangian function.study the Lagrangian multiplier and penalty factor correction formula,and use the filter technique,relax the conditions of acceptance of the trail step,proof of the convergence of the algorithm.Finally,a numerical test.is reported.
作者 夏红卫 陈荣军
机构地区 常州工学院理学院
出处 《数学的实践与认识》 CSCD 北大核心 2010年第20期131-137,共7页 Mathematics in Practice and Theory
基金 江苏省高校自然科学基金(06KJD110011)
关键词 信赖域 拉格朗日乘子 罚因子 滤子技巧 trust-region Lagrangian multiplier penalty factor filter technique
分类号 O224 [理学—运筹学与控制论]
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参考文献11

  • 1Yuan Y X. A review of trust region algorithms for optimization, in: J.M. Ball and J.C.R. Hunt, eds., ICIAM 99: Proceedings of the Fourth International Congress of Industrial and Applied Mathematics, Oxford University Press, 2000, 271-282.
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同被引文献9

  • 1Lawrence C T, Tits A L. A computationally efficient feasible se-quential quadratic programming algorithm [J]. SIAM Journal on Optimization, 2001, 11 (4): 1092-1118.
  • 2Yuan Yaxiang. A review of trust region algorithms for optimiza- tion [C]//Ball J M, Hunt J C R. ICM99: Proceedings of the 4th International Congress on Industial and applied mathematics. Edinburgh: Oxford University Press, 2000: 271-282.
  • 3Powell M J D. Convergence properties of a class of minimization algorithms [C]//Mangassarian O L, Meyer R R, Robinson S M. Nonlinear Programming. New York: Academic Press, 1975: 1-27.
  • 4Chen Lifeng, Goldfarb D. Interior-point 12-penalty methods for nonlinear programming with strong global convergence proper- ties [J]. Math Programming, 2006, 108(1): 1-36.
  • 5Corm A R, Gould N I M, Orban D, et al. A primal-dual trust re- gion algorithm for non-convex nonlinear programming [J]. Math Programming, 2000, 87(2): 215-249.
  • 6Fletcher R, Leyffer S. Nonlinear programming without a penalty function [J]. Math Programming, 2002, 91(2): 239-269.
  • 7Conn A R, Gould N I M, Toint P L. Trust-region methods [M]. Philadephia: SIAM, 2000.
  • 8Conn A R, Gould N I M, Toint P L. Lancelot: a fortran package for large-scale nonlinear optimization [M]. New York: Springer, 1992.
  • 9夏红卫,陈荣军.简单界约束非线性方程组的滤子信赖域法[J].江西师范大学学报（自然科学版）,2009,33(6):661-664. 被引量：1

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数学的实践与认识
2010年 第20期

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