The main motivation of this paper is to weaken the conditions that imply the correspondence between the solution of a constrained problem and the unconstrained minimization of a continuously differentiable function. In particular, a new continuously differentiable exact penalty function is proposed for the solution of nonlinear programming problems. Under mild assumptions, a complete equivalence can be established between the solution of the original constrained problem and the unconstrained minimization of this penalty function on a perturbation of the feasible set. This new penalty function and its exactness properties allow us to define globally and superlinearly convergent algorithms to solve nonlinear programming problems. As an example, a Newton-type algorithm is described which converges locally in one iteration in case of quadratic programming problems.
New Results on a Continuously Differentiable Exact Penalty Function / Lucidi, Stefano. - In: SIAM JOURNAL ON OPTIMIZATION. - ISSN 1052-6234. - STAMPA. - 2:4(1992), pp. 558-574. [10.1137/0802027]
New Results on a Continuously Differentiable Exact Penalty Function
LUCIDI, Stefano
1992
Abstract
The main motivation of this paper is to weaken the conditions that imply the correspondence between the solution of a constrained problem and the unconstrained minimization of a continuously differentiable function. In particular, a new continuously differentiable exact penalty function is proposed for the solution of nonlinear programming problems. Under mild assumptions, a complete equivalence can be established between the solution of the original constrained problem and the unconstrained minimization of this penalty function on a perturbation of the feasible set. This new penalty function and its exactness properties allow us to define globally and superlinearly convergent algorithms to solve nonlinear programming problems. As an example, a Newton-type algorithm is described which converges locally in one iteration in case of quadratic programming problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.