We develop a privacy-preserving distributed algorithm to minimize regularized empirical risk function when the first-order information is not available and data over multi-agent network. employ zeroth-order method associated augmented Lagrangian in primal domain using alternating direction of multipliers (ADMM). show that proposed algorithm, named ADMM (D-ZOA), has intrinsic properties. Most ex...

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting and effects within macroscopic continuum. The behavior is captured via constitutive relations derived from thermodynamic formulation. governing equations of the inhomogeneous continuum are obtained Hamilton principle. As generalization con...