parametric optimal control, saddle point, duality theory, Nonlinear differential equations in abstract spaces, Optimality conditions for problems in abstract spaces, Optimality conditions for minimax problems, Pontryagin maximum principle, minimax optimization problem, Existence theories for problems in abstract spaces, adjoint equation, Duality theory (optimization), nonlinear parametric optimal control, saddle point optimality, Applied Mathematics, evolution triple, necessary conditions, compact embedding, monotone operator, duality, Applications of operator theory in optimization, convex analysis, mathematical programming, economics, Existence of solutions for minimax problems, \(G\)-convergence, Set-valued operators, Analysis, Control problems involving ordinary differential equations