Iterative optimization algorithms for discrete-continuous processes

We propose a series of approximate and iterative optimizational methods for discrete-continuous processes based on Krotov's sufficient optimality conditions. Iterations are constructed by localizing the global optimality conditions and Krotov's minimax scheme with various approximations. The very concept of a discrete-continuous system and the corresponding optimality conditions and algorithms represent a convenient formalism to study a wide class of complex systems and processes, in particular, magistral solutions of singular problems that are significantly non-uniform in structure.