p-Regularity Theory. Tangent Cone Description in the Singular Case

Necessary conditions for weak efficiency for nonsmooth degenerate multiobjective optimization problems

“…It extends to degenerate equality constraints the characterization of the second-order tangent cone due to Pavel-Ursescu [37] given for regular equality constraints. The first-order tangent cones to a degenerate equality constraint set have been described in the literature [38,39]. Only very few types of tangent sets of order greater than one have been described in the degenerate case [29,30].…”

p-regular nonlinearity: tangency at singularity in degenerate optimization problems

“…The proof of Theorem 2.6 can be found in Prusińska and Tretyakov (2016). The importance of this result in the degenerate case is analogous to the importance of the classical implicit function theorem in nondegenerate case.…”

Continuous Dependence of the Singular Nonlinear Van der Pol Equation Solutions with Respect to the Boundary Conditions: Elements of p-regularity Theory

“…In the nonregular case, this theorem cannot be applied. The results obtained in the paper are based on the generalization of the Implicit Function Theorem for nonregular mappings, which were presented, for example, in [1,2,9,10]. We will provide a strong definition of the constructions of p-regularity theory and adapt it to the issue under consideration.…”