Gauss-Seidel-Newton-Armijo approach for minimization problems on the non-negative orthant: Application to spatial price equilibrium problems

Gauss-Seidel-Newton-Armijo approach for minimization problems on the non-negative orthant: Application to spatial price equilibrium problems

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Article ID: iaor19942384
Country: Netherlands
Volume: 57
Issue: 3
Start Page Number: 395
End Page Number: 408
Publication Date: Mar 1992
Journal: European Journal of Operational Research
Authors: , ,
Abstract:

To deal with the optimization problem equ1, the authors propose a Gauss-Seidel type iterative approach where variables are modified sequentially one at a time (GSNA algorithm) or by blocks (BGSNA algorithm). Relying on both the Newton approach and an Armijo rule, an inaccurate line search is performed at each step to determine a step size insuring global convergence. Both robustness (global convergence) and efficiency (rate of local convergence) are analyzed under minimal hypotheses even weaker than those often required to prove the convergence of Gauss-Seidel methods. These procedures are applied to spatial price equilibrium problems, and the numerical results indicate that they are competitive with MINOS.

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