Abstract
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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Bednarczuk, E.M., Tretyakov, A.A. On reductibility of degenerate optimization problems to regular operator equations. Comput. Math. and Math. Phys. 56, 1992–2000 (2016). https://doi.org/10.1134/S0965542516120058
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DOI: https://doi.org/10.1134/S0965542516120058