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A nonlinear programming algorithm based on non-coercive penalty functions

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Abstract.

 We consider first the differentiable nonlinear programming problem and study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function. We associate two parameters to these functions: one is used to control the slope and the other controls the deviation from the exact penalty.

We propose a method that does not change the slope for feasible iterates and show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations. The same results are obtained for non-smooth convex problems under a Slater qualification condition.

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Received: September 2000 / Accepted: June 2002 Published online: March 21, 2003

Research partially supported by CAPES, Brazil

Research partially supported by CNPq, Brazil, and CONICIT, Venezuela.

Mathematics Subject Classification (1991): 20E28, 20G40, 20C20

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Gonzaga, C., Castillo, R. A nonlinear programming algorithm based on non-coercive penalty functions. Math. Program., Ser. A 96, 87–101 (2003). https://doi.org/10.1007/s10107-002-0332-z

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  • DOI: https://doi.org/10.1007/s10107-002-0332-z

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