ZOR - Mathematical Methods of Operations Research (1995) 41:25-55 F~. I ] ['~ A Two Parameter Mixed Interior-Exterior Penalty Algorithm ABDELHAMID BENCHAKROUN 1, JEAN-PIERRE DUSSAULT2 AND ABDELATIF MANSOURI Universit6 de Sherbrooke, Facult6 des sciences, Sherbrooke, Quebec, Canada J1K 2R1, Canada Abstract: In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacr and McCormick using two distinct penalty parameters r, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapo- lation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioningby suitable transformations of the equations, in the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent ~). 0 Introduction Fiacco and McCormick [4], in their classic book, developed a mixed penalty method to solve nonlinear programs rain f(x) s.t. 9(x) < 0 (0.1) h(x) = 0 where f: •" ~ R, O: R" ~ R" and h: R" ~ R p. The method consists in solving a sequence of unconstrained problems 1 ~h~(x), min f(x) -- r k log(--Oi(x)) -t- ~rk j=l x•R n i=1 if(x) < 0 (0.2) Research partially supported by NSERC grant OGP0036512. 2 Research partially supported by NSERC grant OGP0005491. 0340- 9422/95/41 : 1/25 - 55 $2.50 9 1995 Physica-Verlag, Heidelberg