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 ...

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...

There is a natural linkage between the molecular structures and the bio-medical and pharmacology characteristics. A topological index can be considered as transformation of chemical structure in to real number and has been used as a predictor parameter. There are certain vertex-degree-based topological indices which has been used extensively in the chemical graph theory but recently no further ...

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...

In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of the underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of admissible controls under this problem setup. Specifically, we establish a rigorous first order approximation of the value function associated to a fixed zero...

Asynchronous parallel optimization received substantial successes and extensive attention recently. One of core theoretical questions is how much speedup (or benefit) the asynchronous parallelization can bring to us. This paper provides a comprehensive and generic analysis to study the speedup property for a broad range of asynchronous parallel stochastic algorithms from the zeroth order to the...

Federated learning (FL), as an emerging edge artificial intelligence paradigm, enables many devices to collaboratively train a global model without sharing their private data. To enhance the training efficiency of FL, various algorithms have been proposed, ranging from first-order second-order methods. However, these cannot be applied in scenarios where gradient information is not available, e....