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...

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

Rough stochastic volatility models have attracted a lot of attention recently, in particular for the linear option pricing problem. In this talk, I will start with power utilities, and propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index H ∈ (0, 1...

The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

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...

We present the first observations of zero-n[over ] band gaps in photonic crystal superlattices consisting of alternating stacks of negative-index photonic crystals and positive-index dielectric materials in the near-infrared range. Guided by ab initio three-dimensional numerical simulations, the fabricated nanostructured superlattices demonstrate the presence of zeroth-order gaps in remarkable ...

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...