On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming

• Autores: Laureano Fernando Escudero Bueno
• Localización: Questiió: Quaderns d'Estadística, Sistemes, Informatica i Investigació Operativa, ISSN 0210-8054, Vol. 6, Nº. 4, 1982, págs. 333-349
• Idioma: inglés
• Títulos paralelos:
  • Precondicionamiento diagonal del método BFGS de 2 etapas con etapas acumuladas para programación no lineal restringida linealmente en supraescala
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We present an algorithm for supra-scale linearly constrained nonlinear programming (LNCP) based on the Limited-Storage Quasi-Newton's method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced Truncated-Newton methodology, that has been proved to be satisfactory for super-scale problems, is not recommended for supra-scale problems since it requires an additional gradient evaluation and the solving of two systems of linear equations per each minor iteration. It is recommended a 2-steps BFGS approximation of the inverse of the reduced Hessian matrix such that it does not require to store any matrix since the product matrix-vector is the vector to be approximated; it uses the reduced gradient and solution related to the two previous iterations and the so-termed restart iteration. A diagonal direct BFGS preconditioning is used