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AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY 被引量:1

AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY
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摘要 An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations. An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
出处 《Journal of Computational Mathematics》 SCIE CSCD 2018年第3期331-350,共20页 计算数学(英文)
关键词 Nonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence. Nonlinear constrained optimization Augmented Lagrangian function Bi-object strategy Global convergence.
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  • 1R.H. Byrd, R.B. Schnabel and G.A. Shultz, A trust region algorithm for nonlinearly constrained optimization, SIAM J. Numer. Anal., 24 (1987), 1152-1170.
  • 2M.R. Celis, J.E. Dennis and R.A. Tapia, A trust region algorithm for nonlinear equality constrained optimization, in: P.T. Boggs, R.H. Byrd and R.B. Schnabel, eds., Numerical Optimization, SIAM, Philadelphia, USA, 1985.
  • 3L. Chen and D. Goldfarb, Interior point l2-penalty methods for nonlinear programming with strong global convergence properties, Math. Program., 108 (2006), 1-36.
  • 4T.F. Coleman and Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optimiz., 6 (1996), 418-445.
  • 5A.R. Conn, N.I.M. Gould, D. Orban and Ph.L. Toint, A primal-dual trust region algorithm for non-convex nonlinear programming, Math. Program., 87 (2000), 215-249.
  • 6A.R. Conn, N.I.M. Gould and Ph.L. Toint, LANCELOT: a Fortran package for large-scale nonlinear optimization (Release A), Springer, Heidelberg, New York. USA, 1992.
  • 7A.R. Conn, N.I.M. Gould and Ph.L. Toint, Trust-Region Methods, SIAM, Philadelphia, USA, 2000.
  • 8J.E. Dennis and H.H.W. Mei, Two new unconstrained optimizaiton algorithms which use function and gradient values, J. Optimiz. Theory App., 28 (1979), 453-482.
  • 9E.D. Dolan and J.J. More, Benchmarking optimization software with performance profiles. Math. Program., Serial A., 91 (2002), 201-213.
  • 10R. Fletcher, A model algorithm for composite NDO problem, Math. Program. Study, 17 (1982), 67-76.

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