Title: An Interior-point L1-penalty Method for Nonlinear Optimization



			   Dominique Orban
	Department of Mathematics and Industrial Engineering
		  Ecole Polytechnique de Montreal
		    2900 Blvd Edouard Montpetit
		    Montreal, QC H3T-1J4 Canada
	             Dominique.Orban@polymtl.ca
		 


Abstract:
A  mixed interior/exterior-point method  for nonlinear  programming is
described,  that handles  constraints  by an  L1-penalty function.   A
suitable  decomposition of  the  penalty terms  and  embedding of  the
problem  into a  higher-dimensional  setting leads  to an  equivalent,
surprisingly regular,  reformulation as a smooth  penalty problem only
involving inequality  constraints. The  resulting problem may  then be
tackled using interior-point techniques as finding a strictly feasible
initial point is trivial.  The  reformulation relaxes the shape of the
constraints, promoting larger steps and easing the nonlinearity of the
strictly feasible  set in the  neighbourhood of a solution.  Under the
Mangasarian--Fromovitz  constraint  qualification,  exactness  of  the
penalty  function  eliminates  the  need to  drive  the  corresponding
penalty parameter  to infinity. Global  and fast local  convergence of
the  proposed scheme  are  established and  practical  aspects of  the
method are discussed.