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.
1992
constrained optimization; nonlinear programming algorithms; nonlinear programming theory
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/16409
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