Open AccessOptimality properties of an Augmented Lagrangian method on infeasible problems
Author(s) -
Ernesto G. Birgin,
J. M. Martı́nez,
L. F. Prudente
Publication year - 2014
Publication title -
computational optimization and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.028
H-Index - 78
eISSN - 1573-2894
pISSN - 0926-6003
DOI - 10.1007/s10589-014-9685-5
Subject(s) - mathematics , mathematical optimization , augmented lagrangian method , nonlinear programming , set (abstract data type) , lagrangian , point (geometry) , measure (data warehouse) , function (biology) , nonlinear system , interior point method , algorithm , computer science , physics , geometry , evolutionary biology , quantum mechanics , database , programming language , biology
Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the other hand, one may wish to find a point with minimal infeasibility for which some optimality condition, with respect to the objective function, holds. Ideally, the algorithm should converge to a minimizer of the objective function subject to minimal infeasibility. In this paper the behavior of an Augmented Lagrangian algorithm with respect to those properties will be studied.
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