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Superlinear Exact penalty Algorithms with Structured Projected Hessian Updates in Broyden’s Family for Constrained Nonlinear Least squares

Bidabadi, Narges | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 43119 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi-Amiri, Nezamoddin
  7. Abstract:
  8. Due to the special structure of the Hessian matrix in nonlinear least squares problems,use of effective structured updating schemes for approximating the Hessian matrix in solving such problems has been considered. Mahdavi-Amiri and Bartels used a structured BFGS method for approximating the projected Hessian matrix in solving constrained nonlinear least squares (CNLLS) problems. Recently, Mahdavi-Amiri and Ansari applied other structured DFP and BFGS methods for approximating the projected Hessian matrix in solving CNLLS problems and proved both global and asymptotic two-step superlinearconvergence of the algorithms. Here, we present other methods for approximating the structured projected Hessian matrix. We first establish sufficient conditions for an asymptotic two-step superlinearly convergence of a structured projected Hessian matrix update formula corresponding to an exact penalty algorithm for solving CNLLS problems. Then, we present some structured updating schemes for the PSB, DFP, BFGS and Broyden’s methods, in general, satisfying these conditions, and hence admitting an asymptotic two-step superlinear
    convergence of the proposed algorithms.We also show global convergence of the algorithms under seasonable assumptions. The numerical results obtained by an implementation of our algorithms in MATLAB 7.6 environment, compared with the ones obtained by three algorithms in the KNITRO software package and the fmincon function in MATLAB, confirm the competetiveness of the proposed algorithms
  9. Keywords:
  10. Exact Penalty Function ; Projected Structured Hessian Update ; Constrained Nonlinear Least Squares ; Asymptotic Two-Step Superlinear Convergence

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