Abstract <p>On the basis joint use of optimal control methods, nonlinear analysis, and the theory of ill-posed problems, the regularization of the Lagrange principle (LP) in nondifferential form, in regular and irregular variants, in a nonlinear (nonconvex) optimization problem of a general Goursat–Darboux system with a pointwise state equality constraint is considered. This constraint is understood as equality in the Hilbert space of square-summable functions and contains an additive parameter, which makes it possible to use the nonlinear version of the perturbation method for studying the problem. The main purpose of both variants of the regularized LP is the stable generation of generalized minimizing sequences (GMS) in the problem under consideration the existence of a solution to which is not assumed a priori. They can be interpreted as GMS-forming (regularizing) operators that associate with each set of initial data of the problem a subminimizer (minimizer) of its regular augmented Lagrangian (AL) corresponding to this set the dual variable in which is generated in accordance with the procedures specified in these variants. The construction of the ALs is completely determined by the type of nonlinear subdifferentials of a lower semicontinuous and, generally speaking, nonconvex value function considered as a function of the problem parameter. As these subgradients, the proximal subgradient and the Fréchet subdifferential, which are well known in nonlinear analysis, are used. In the special case of a regular (in the sense of the existence of a generalized Kuhn–Tucker vector in it) problem and its initial data (the integrand of the objective functional and the right-hand side of the controlled system) depend affinely on the control, the passage to limit in the relations of the regularized LP leads to classical optimality conditions in the form of the nondifferential Kuhn–Tucker theorem and the Pontryagin maximum principle.</p>