First order logic without quantifiers, a.k.a. zeroth order logic, is more expressive than propositional logic. In this paper, we introduce two new operators for regular expressions allowing us to handle zeroth order boolean formula in order to increase the expressive power of expressions; We also extend the notion of interpretation and of realization using expression interpretation. We thus def...

In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being over n agents having access only to zeroth-order (ZO) information of cost. This has various machine learning applications. As solution, propose two ZO algorithms, in which at each iteration agent samples local oracle points time-varying smoothing parameter. We show that proposed algor...

We consider stochastic zeroth-order optimization over Riemannian submanifolds embedded in Euclidean space, where the task is to solve problems with only noisy objective function evaluations. Toward this, our main contribution propose estimators of gradient and Hessian from evaluations, based on a version Gaussian smoothing technique. The proposed overcome difficulty nonlinearity manifold constr...

We consider the problem of minimizing a smooth, Lipschitz, convex function over compact, set using sub-zeroth-order oracles: an oracle that outputs sign directional derivative for given point and direction, compares values pair points, noisy value point. show sample complexity optimization these oracles is polynomial in relevant parameters. The algorithm we provide comparator first with known r...

We discuss some features of the orthogonalization methods commonly applied to QSPR QSAR studies. We outline the well known multivariable linear regression analysis in vector form in order to compare mainly Randic and Gram-Schmidt orthogonalization procedures and also cast the basis for other approaches like Löwdin’s one. We expect that present review may become the starting point for future dev...

In this research paper, we will compute the topological indices (degree based) such as ordinary generalized geometric-arithmetic (OGA) index, first and second Gourava indices, hyper-Gourava general Randic´ index R γ G ,</mo...

In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via calls to a stochastic first-order or zeroth-order oracle. In each iteration of the proposed methods, we minimize an exact penalty function which is nonsmooth an...

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 ...