Sensitivity analysis for equilibrium problems and applications to optimal control problems

In this paper, we consider parametric set-valued equilibrium problems in normed spaces. By employing the direct approach based on generalized convexity and monotonicity assumptions, we establish Hölder/Lipschitz conditions for both exact and approximate efficient solutions of the reference problems. We demonstrate that with this approach, the commonly required additional conditions of indirect methods, such as scalarization methods, as seen in existing works, can be avoided. Utilizing the proposed approach and techniques, we also derive Lipschitz conditions for two optimal control models in biology and economics: one describing the interaction between a predator and its prey, and another addressing the balance between holding cash and investing.