Abstract In this paper, we consider stochastic weakly convex optimization problems, however without the existence of a subgradient oracle. We present derivative free algorithm that uses two point approximation for computing gradient estimate smoothed function. prove convergence at similar rate as state art methods, with larger constant, and report some numerical results showing effectiveness ap...

Materials with nanoscale phase separation are considered. A system representing a heterophase mixture of ferromagnetic and paramagnetic phases is studied. After averaging over configurations, renormalized Hamiltonian derived describing the coexisting phases. The characterized by direct exchange interactions an external magnetic field. properties studied numerically. stability conditions define ...

The four laws of black hole mechanics have been put forward for a long time. However, the zeroth law, which states that surface gravity stationary is constant on event horizon, still lacks universal proof in various modified gravitational theories. In this paper, we study law {in special Horndeski gravity}, an interesting theory with nonminimally coupled scalar field. After assuming {the field ...

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...

In this paper, we prove new complexity bounds for zeroth-order methods in non-convex optimization with inexact observations of the objective function values. We use Gaussian smoothing approach Nesterov and Spokoiny(Found Comput Math 17(2): 527–566, 2015. https://doi.org/10.1007/s10208-015-9296-2 ) extend their results, obtained smooth problems, to setting minimization functions Hölder-continuou...

What is now known as the zeroth "law" of thermodynamics was first stated by Maxwell in 1872: at equilibrium, "Bodies whose temperatures are equal to that of the same body have themselves equal temperatures." In the present paper, we give an explicit mathematical proof of the zeroth "law" for classical, deterministic, T-mixing systems. We show that if a body is initially not isothermal it will i...