This paper presents an analysis of the involvement of the penalty parameter in exact penalty function methods that yields modiications to the standard outer loop which decreases the penalty parameter (typically dividing it by a constant). The procedure presented is based on the simple idea of making explicit the dependence of the penalty function upon the penalty parameter and is illustrated on...

First, this paper introduces a notion of a sharp penalty mapping which can replace more common exact penalty function for convex feasibility problems. Second, it uses it for solution of variational inequalities with monotone operators or pseudo-varitional inequalities with oriented operators. Appropriately scaled the sharp penalty mapping can be used as an exact penalty in variational inequalit...

We propose a Gauss-Newton-type method for nonlinear constrained optimization using the exact penalty introduced recently by André and Silva for variational inequalities. We extend their penalty function to both equality and inequality constraints using a weak regularity assumption, and as a result, we obtain a continuously differentiable exact penalty function and a new reformulation of the KKT...

Exact penalty approach aims at replacing a constrained optimization problem by an equivalent unconstrained optimization problem. Most of results in the literature of exact penalization are mainly concerned with finding conditions under which a solution of the constrained optimization problem is a solution of an unconstrained penalized optimization problem and the reverse property is rarely stud...

Exact penalty methods for the solution of constrained optimization problems are based on the construction of a function whose unconstrained minimizing points are also solution of the constrained problem. In the rst part of this paper we recall some deenitions concerning exactness properties of penalty functions, of barrier functions, of augmented Lagrangian functions, and discuss under which as...

Line search algorithms for nonlinear programming must include safeguards to enjoy global convergence properties. This paper describes an exact penalization approach that extends the class of problems that can be solved with line search SQP methods. In the new algorithm, the penalty parameter is adjusted at every iteration to ensure sufficient progress in linear feasibility and to promote accept...

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, ...