Geodesic
On reductibility of degenerate optimization problems to regular operator equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12 
E. Bednarczuk; A. Tretyakov. On reductibility of degenerate optimization problems to regular operator equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a2/
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     title = {On reductibility of degenerate optimization problems to regular operator equations},
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     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We present an application of the $p$-regularity theory to the analysis of non-regular (irregular, degenerate) nonlinear optimization problems. The $p$-regularity theory, also known as the $p$-factor analysis of nonlinear mappings, was developed during last thirty years. The $p$-factor analysis is based on the construction of the $p$-factor operator which allows us to analyze optimization problems in the degenerate case. We investigate reducibility of a non-regular optimization problem to a regular system of equations which do not depend on the objective function. As an illustration we consider applications of our results to non-regular complementarity problems of mathematical programming and to linear programming problems.

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