Geodesic
On reductibility of degenerate optimization problems to regular operator equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 12

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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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     author = {E. Bednarczuk and A. Tretyakov},
     title = {On reductibility of degenerate optimization problems to regular operator equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {56},
     number = {12},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_12_a2/}
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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/