An exact penalty function method with global convergence properties for nonlinear programming problems.(English)Zbl 0631.90061
In the paper a new continuously differentiable exact penalty function is given for the solution of nonlinear programming problems with compact feasible set. Continuously differentiable exact penalty functions were introduced byR. Fletcher [in: Integer nonlin. Program., 157-175 (1970;Zbl 0332.90039)] for the equality constrained case; the extension to the inequality constrained case has been studied byT. Glad andE. Polak [Math. Program. 17, 140-155 (1979;Zbl 0414.90078)] and by the authors [SIAM J. Control Optimization 23, 72-84 (1985;Zbl 0569.90072)].
It is proved that under suitable regularity and compactness assumptions, a complete equivalence can be established between the solution of a constrained nonlinear programming problem and the unconstrained minimization of a differentiable function whose local minimizers are contained in a bounded open set.
Also a globally convergent algorithm is defined which cannot produce unbounded sequences, thus overcoming the main drawback of existing algorithms based on exact penalty functions.
It is proved that under suitable regularity and compactness assumptions, a complete equivalence can be established between the solution of a constrained nonlinear programming problem and the unconstrained minimization of a differentiable function whose local minimizers are contained in a bounded open set.
Also a globally convergent algorithm is defined which cannot produce unbounded sequences, thus overcoming the main drawback of existing algorithms based on exact penalty functions.
Reviewer: W.Kotarski
MSC:
| 90C30 | Nonlinear programming |
| 49M30 | Other numerical methods in calculus of variations (MSC2010) |
| 65K05 | Numerical mathematical programming methods |
| 49M37 | Numerical methods based on nonlinear programming |
Cite
Full Text:DOI
References:
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