Regularization of degenerated equations and inequalities under explicit data parameterization

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Abstract
- The regularization problem of degenerated nonlinear system of equations/ inequalities in Banach spaces is considered. The proposed approach is based on the explicit parametrization of input data and on the utilization of the multi-valued mapping techniques. Two regularization methods are suggested: the extended minimization and the regularized partial penalty function one. According to the first method an ill-posed problem should be replaced by a search of the minimal norm element in the join of solution sets of the family of problems that are equivalent to the initial one with respect to input data accuracy. The second one is based on separation from the initial system some regular part. Suggested approach is illustrated on some examples (analytical and numerical), including a singular system of ordinary differential and finite equations.

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