abstract
- There is a substantial literature treating the question of uniqueness of Lagrange multipliers in mathematical programming, as well as that of finding useful characterizations and deriving some of its consequences. However, little attention has been paid to the same question in optimal control, and not until recently the problem of how to characterize the uniqueness of multipliers for certain classes of optimal control problems involving equality and inequality constraints in the control functions was solved. The objective in this paper is twofold. On one hand, we generalize previously obtained characterizations to problems with mixed state-control constraints, indicating which results are no longer valid in this context, and on the other hand, we derive new characterizations of the uniqueness and boundedness of multipliers related to concepts such as viability theory and observability of systems. © 2025, American Institute of Mathematical Sciences. All rights reserved.