NLPQLP - Nonlinear Programming with Non-Monotone and Distributed Line Search. NLPQLP is a special implementation of a sequential quadratic programming (SQP) method. Proceeding from a quadratic approximation of the Lagrangian function and a linearization of constraints, a quadratic programming subproblem is formulated and solved by QL. Depending on the number of nodes of the distributed system, objective and constraint functions can be evaluated simultaneously at predetermined test points along the search direction. The parallel line search is performed with respect to an augmented Lagrangian merit function. Moreover, a non-monotone line search is performed in error situations where the line search cannot be stopped within a given number of iterations. All theoretical convergence properties of the SQP algorithm remain satisfied. The Hessian approximation is updated by the modified BFGS-formula. The new version is extremely stable. Various restarts options are implemented to overcome error situations, which usually lead to termination. It is possible to solve 90 % of our 306 standard test examples even if the partial derivatives possess only one correct digit due to random noise.

References in zbMATH (referenced in 28 articles , 1 standard article )

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  1. Gould, Nicholas I.M.; Orban, Dominique; Toint, Philippe L.: CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization (2015)
  2. Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong Hong: Optimal control problems with stopping constraints (2015)
  3. Lin, Qun; Loxton, Ryan; Xu, Chao; Teo, Kok Lay: Parameter estimation for nonlinear time-delay systems with noisy output measurements (2015)
  4. Sachsenberg, Björn; Schittkowski, Klaus: A combined SQP-IPM algorithm for solving large-scale nonlinear optimization problems (2015)
  5. Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong Hong: Optimal feedback control for dynamic systems with state constraints: an exact penalty approach (2014)
  6. Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong Hong; Yu, Changjun: A new exact penalty method for semi-infinite programming problems (2014)
  7. Liu, Chongyang; Loxton, Ryan; Teo, Kok Lay: A computational method for solving time-delay optimal control problems with free terminal time (2014)
  8. Liu, Chongyang; Loxton, Ryan; Teo, Kok Lay: Optimal parameter selection for nonlinear multistage systems with time-delays (2014)
  9. Östermark, Ralf: A parallel fuzzy GMM-algorithm for approximate VGARCH-modeling with a multi-modal discontinuous merit function (2014)
  10. Jiang, Canghua; Lin, Qun; Yu, Changjun; Teo, Kok Lay; Duan, Guang-Ren: An exact penalty method for free terminal time optimal control problem with continuous inequality constraints (2012)
  11. Lin, Qun; Loxton, Ryan; Teo, Kok Lay; Wu, Yong Hong: Optimal control computation for nonlinear systems with state-dependent stopping criteria (2012)
  12. M’Hallah, Rym; Alkandari, Abdulaziz: Packing unit spheres into a cube using VNS (2012)
  13. Wang, Ling Yun; Gui, Wei Hua; Teo, Kok Lay; Loxton, Ryan; Yang, Chun Hua: Optimal control problems arising in the zinc sulphate electrolyte purification process (2012)
  14. Schittkowski, K.: A robust implementation of a sequential quadratic programming algorithm with successive error restoration (2011)
  15. Amoignon, Olivier: AESOP---a numerical platform for aerodynamic shape optimization (2010)
  16. Loxton, R.C.; Teo, K.L.; Rehbock, V.; Ling, W.K.: Optimal switching instants for a switched-capacitor DC/DC power converter (2009)
  17. Loxton, R.C.; Teo, K.L.; Rehbock, V.; Yiu, K.F.C.: Optimal control problems with a continuous inequality constraint on the state and the control (2009)
  18. Schittkowski, Klaus: An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints (2009)
  19. Dai, Yu-Hong; Schittkowski, Klaus: A sequential quadratic programming algorithm with non-monotone line search (2008)
  20. Lachiheb, Mehdi; Smaoui, Hichem: A simple decomposition based SQP algorithm for large scale nonlinear programming (2008)

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