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一般约束非线性优化的增广Lagrangian算法 被引量:2

An Augmented Lagrangian Algorithm for Optimization with General Constraints
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摘要 构造了一个求解一般约束非线性优化问题的增广Lagrangian算法 ,通过引进函数 φ(x) =max{g(x) ,- λr}可直接处理不等式的约束情形 .并且每次只需近似地求出对应增广Lagrangian罚函数的局部最小点 .在一般假设下 ,算法产生的点列的任意聚点都是问题的K The paper presents an augmented lagrangian algorithm for optimization with general constraints. By applying to the function φ(x)=max{g(x),-λr} , the algorithm can be applied directly in the case of inequality constraints. At any iteration, it only needs to get an approximate local minimum of the augmented lagrangian penalty fiction. Under general assumptions, the algorithm converges to the K-T point of the problem.
出处 《湘南学院学报》 2004年第5期31-34,43,共5页 Journal of Xiangnan University
关键词 算法 线性优化 优化问题 非线性 不等式 函数 求解 近似 augmented lagrangian function inequality constraints K-T point
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参考文献4

  • 1[1]A.R.Conn,Nick Gould,A.Sartenaer and Ph.L.Toint.Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints.[EB/OL].http://www.doc.cern.ch/tmp/convert-SCAN-9503091.pdf.
  • 2[2]A.R.Conn, Nick Gould, A.Sartenaer and Ph.L.Toint. Global convergence properties of two augmented Lagrangian algorithms for optimization with a combination of general equality and linear constraints. Tvehnical Report TR/PA/93/26,CERFACS,Toulonse,France,1993a.
  • 3[3]Robert Michael Lewis, Virginia Torczom. A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds[J]. SIAM J.Optim.2002,12(4):1075-1089.
  • 4童小娇,周叔子.等式与界约束非线性优化的信赖域增广Lagrangian算法[J].计算数学,2002,24(1):27-28. 被引量:2

二级参考文献3

  • 1Francisco A. M. Gomes,María Cristina Maciel,José Mario Martínez. Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters[J] 1999,Mathematical Programming(1):161~200
  • 2J. F. Rodrigues,J. E. Renaud,L. T. Watsen. Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data[J] 1998,Structural Optimization(3-4):141~156
  • 3Thomas F. Coleman,Yuying Li. On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds[J] 1994,Mathematical Programming(1-3):189~224

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