Generalized implicit function theorem and its application to parametric optimal control problems

Many problems in physics and mathematics may be reduced to solving equations depending on a parameter. The justification of the existence of solutions to the equations and the sensitivity analysis may be conducted based on Implicit Function Theorem (IFT) under certain regularity assumptions. Provided the regularity assumptions do not hold, generalizations of IFT are needed in order to study solutions to the equations. The paper focuses on a particular generalization of IFT which is then applied to a parametric linear time-optimal control problem.