We present the main concept and results of the p-regularity theory (also known as p-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of p-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and p- order necessary and sufficient optimality conditions. We substantiate the rate of convergence of p-factor method.
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The paper presents recent advances in p-regularity theory. The main result of this theory gives a detailed description of the structure of the zero set of an irregular nonlinear mapping. We illustrate the theory with an application to the problem of existence of the solutions to the nonlinear equations with singular mappings.
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