Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization

Gilbert J-C (1991). Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization. Mathematical Programming 50 (1-3): 1-28. DOI:10.1007/BF01594922.

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Abstract

We propose an algorithm for minimizing a function f on ℝn in the presence of m equality constraints c that locally is a reduced secant method. The local method is globalized using a nondifferentiable augmented Lagrangian whose decrease is obtained by both a longitudinal search that decreases mainly f and a transversal search that decreases mainly ∥c∥. Our main objective is to show that the longitudinal path can be designed to maintain the positive definiteness of the reduced matrices by means of the positivity of γk Tδk, where γk is the change in the reduced gradient and δk is the reduced longitudinal displacement.

Item Type: Article
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: Romeo Molina
Date Deposited: 21 Apr 2016 14:29
Last Modified: 21 Apr 2016 14:29
URI: http://pure.iiasa.ac.at/12880

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