A nonlinear programming algorithm based on non-coercive penalty functions

 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. 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