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Linear and non-linear programming software validity

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  • Tolla, Pierre

Abstract

The numerical software users are often perturbed by accuracy problems imputable to the rounding errors generated by computer hardware. M. La Porte and J. Vignes (4) created the permutation-perturbation method for evaluating the validity of the solutions of linear algebraic systems, detection of the matrix singularity, and optimal termination criterion of iteratives methods. These problems exist and are considerably amplified in linear and non-linear programming algorithms using near simplex methods : Reduced Gradient of P. Wolfe and Generalized Reduced Gradient of J. Abadie (1) ; effectively, these methods proceed with a long sequence of matrix inversions which increases rounding errors, and it is not unu4sual to obtain false basic solutions or singular basic matrices. Moreover, the classical termination criterions of unconstrained optimization may involve either an untimely stop of the algorithm producing a solution far from the optimum, or, on the contrary, a large number of unprofitable iterations which does not improve the current solution. I suggest, in this paper, some quick and efficient procedures for solving these problems.

Suggested Citation

  • Tolla, Pierre, 1983. "Linear and non-linear programming software validity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(1), pages 39-42.
    • Handle: RePEc:eee:matcom:v:25:y:1983:i:1:p:39-42
    DOI: 10.1016/0378-4754(83)90028-9
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    Cited by:

    1. Vignes, J., 1988. "Review on stochastic approach to round-off error analysis and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 481-491.
    2. Vignes, Jean, 1984. "An efficient implementation of optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(3), pages 243-256.
    3. Alliot, Nicole, 1988. "Data error analysis in unconstrained optimization problems with the CESTAC method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(6), pages 531-539.
    4. Vignes, J., 1993. "A stochastic arithmetic for reliable scientific computation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(3), pages 233-261.

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