On the compatibility of classical multiplier estimates with variable reduction techniques when there are nonlinear inequality constraints

• Autores: Eugenio Juan Mijangos Fernández, Narcís Nabona Francisco
• Localización: Questiió: Quaderns d'Estadística, Sistemes, Informatica i Investigació Operativa, ISSN 0210-8054, Vol. 23, Nº. 1, 1999, págs. 61-83
• Idioma: inglés
• Títulos paralelos:
  • Compatibilidad de estimaciones clásicas de multiplicadores con técnicas de reducción variable cuando existen restricciones de desigualdad no lineal
• Enlaces
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• Resumen

  • The minimization of a nonlinear function subject to linear and nonlinear equality constraints and simple bounds can be performed through minimizing a partial augmented Lagrangian function subject only to linear constraints and simple bounds by variable reduction techniques. The first-order procedure for estimating the multiplier of the nonlinear equality constraints through the Kuhn-Tucker conditions is analyzed and compared to that of Hestenes-Powell. There is a method which identifies those major iterations where the procedure based on the Kuhn-Tucker conditions can be safely used and also computes these estimates. This work justifies the extension of the former results to the case of general inequality constraints. To this end two procedures that convert inequalities into equalities are considered