A Global Convergence Theory for the Celis–Dennis–Tapia Trust-Region Algorithm for Constrained Optimization | Zendy

Mahmoud El-Alem | Zendy

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A Global Convergence Theory for the Celis–Dennis–Tapia Trust-Region Algorithm for Constrained Optimization

Author(s) -

Mahmoud El-Alem

Publication year - 1991

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/0728015

Subject(s) - mathematics , trust region , convergence (economics) , symbolic convergence theory , augmented lagrangian method , penalty method , cauchy distribution , quadratic equation , mathematical optimization , scheme (mathematics) , function (biology) , algorithm , quadratic model , computer science , mathematical analysis , geometry , evolutionary biology , key (lock) , economics , radius , biology , statistics , response surface methodology , computer security , economic growth

A global convergence theory for a class of trust-region algorithms for solving the equality constrained optimization problem is presented. This theory is sufficiently general that it holds for any algorithm that generates steps giving at least a fraction of Cauchy decrease in the quadratic model of the constraints, and that uses the augmented Lagrangian as a merit function. This theory is used to establish global convergence of the 1984 Celis–Dennis–Tapia algorithm with a different scheme for updating the penalty parameter. The behavior of the penalty parameter is also discussed.

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