Geodesic
On the application of the residual method for the correction of inconsistent problems of convex programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 268-276

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For the correction of a convex programming problem with potentially inconsistent constraint system (an improper problem), we apply the residual method, which is a standard regularization procedure for ill-posed optimization models. Further, a problem statement typical for the residual method is reduced to the minimization problem for an appropriate penalty function. We apply two classical penalty functions: the quadratic penalty function and the Eremin–Zangwill exact penalty function. For each of the approaches, we establish convergence conditions and estimates for the approximation error.
Keywords: convex programming, improper problem, residual method, penalty function methods.
Mots-clés : optimal correction 
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     author = {V. D. Skarin},
     title = {On the application of the residual method for the correction of inconsistent problems of convex programming},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {268--276},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/}
}
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V. D. Skarin. On the application of the residual method for the correction of inconsistent problems of convex programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 268-276. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a22/