In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these zeroth-order (ZO) methods that only need function often more efficient than FO sometimes the options. this paper, we propose a novel inexact augmented Lagrangian method (ZO-iALM) to solve black-box optimization which involve composite (i.e., smooth+nonsmooth) objective ...

We present Free-MESSAGEp, the first zeroth-order algorithm for convex mean-semideviation-based risk-aware learning, which is also three-level compositional stochastic optimization algorithm, whatsoever. Using a non-trivial extension of Nesterov's classical results on Gaussian smoothing, we develop Free-MESSAGEp from principles, and show that it essentially solves smoothed surrogate to original ...

The size consistency of multi-reference Møller-Plesset perturbation theory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection operators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of projection operators onto particular subspaces, cros...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.

Functionally constrained stochastic optimization problems, where neither the objective function nor constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have access to noisy evaluations of and functions, propose analyze zeroth-order algorithms for solving class problem. When domain is [Formula: see text], there m esta...