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

Gilbert JC (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 functionf on ℝn in the presence ofm equality constraintsc 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 mainlyf 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 ofγkTδk, whereγk is the change in the reduced gradient and δk is the reduced longitudinal displacement.

Item Type: Article
Uncontrolled Keywords: Augmented Lagrangian; constrained optimization; exact penalty function; global convergence; optimization algorithm; reduced secant method; superlinear convergence; Wolfe's step-size selection
Research Programs: Methodology of Decision Analysis (MDA)
Depositing User: Romeo Molina
Date Deposited: 14 Dec 2016 12:47
Last Modified: 14 Dec 2016 12:47
URI: http://pure.iiasa.ac.at/14158

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