This paper presents an innovative optimization strategy for enhancing the seismic retrofitting of inelastic Moment Resisting Frames (MRFs) equipped with nonlinear Fluid Viscous Dampers (FVDs) and Negative Stiffness Devices (NSDs), with a particular focus on irregular structures. The primary objective of this approach is to minimize a cost-related function that encompasses expenses linked to the supplemental FVDs and NSDs. The method concurrently optimizes the mechanical traits and spatial arrangement of both FVDs and NSDs, efficiently utilizing differentiable functions for a gradient-based optimization technique. Adhering to computational efficiency, gradients are determined through adjoint sensitivity analysis. The structural response assessment employs Nonlinear Time History Analysis (NTHA), accommodating the nonlinearity of MRF elements, FVDs, and NSDs. The PEER framework is adopted to introduce a performance constraint using loss estimation analysis. A practical case study underscores the efficacy of this methodology, highlighting its capacity to minimize costs while considering seismic performance and nonlinear behavior. This optimization approach stands as a powerful tool for seismic retrofitting, capitalizing on the combined advantages of FVDs and NSDs for irregular structures, while offering computational efficiency for real-world implementation.