A rapidly convergent method for equality constrained function minimization

This paper presents a new function minimization algorithm for minimizing nonlinear functions of a finite number of variables subject to nonlinear equality constraints. The algorithm also provides for the explicit handling of upper and lower bounds on each of the independent variables. Although other...

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Bibliographic Details
Published in1973 IEEE Conference on Decision and Control including the 12th Symposium on Adaptive Processes pp. 80 - 81
Main Author Brusch, R. G.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.1973
Subjects
Application software
Constraint optimization
Constraint theory
Convergence
Minimization methods
Optimal control
Publishing
Testing
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DOI10.1109/CDC.1973.269134

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Summary:This paper presents a new function minimization algorithm for minimizing nonlinear functions of a finite number of variables subject to nonlinear equality constraints. The algorithm also provides for the explicit handling of upper and lower bounds on each of the independent variables. Although other more general inequality constraint can be transformed into an equality constraint at the expense of introducing an additional slack variable. The algorithm proposed combines the idea of a "balance function," developed independently in References 1 and 2 with a second order method for updating the balance function La grange multipliers originally developed in Reference 3. This updating technique makes use of the current estimate of the inverse Hessian of the balance function which is a byproduct of the unconstrained minimization of the balance function using the Fletcher-Powell algorithm.
DOI:10.1109/CDC.1973.269134