In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs fxk; ¸kg converging quadratically to a pair (¹x;¹¸) where ¹x satisfies the first order necessary conditions and ¹¸ is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence fxkg alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported

A shifted-barrier primal-dual algorithm model for linearly constrained optmization problems / DI PILLO, Gianni; Lucidi, Stefano; Palagi, Laura. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 12:(1999), pp. 157-188. [10.1023/A:1008675917367]

A shifted-barrier primal-dual algorithm model for linearly constrained optmization problems

DI PILLO, Gianni;LUCIDI, Stefano;PALAGI, Laura
1999

Abstract

In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs fxk; ¸kg converging quadratically to a pair (¹x;¹¸) where ¹x satisfies the first order necessary conditions and ¹¸ is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence fxkg alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported
linearly constrained optimization; primal-dual algorithm; Penalty-Lagrangian merit function
01 Pubblicazione su rivista::01a Articolo in rivista
A shifted-barrier primal-dual algorithm model for linearly constrained optmization problems / DI PILLO, Gianni; Lucidi, Stefano; Palagi, Laura. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 12:(1999), pp. 157-188. [10.1023/A:1008675917367]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/250278
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