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...

In this paper, we evaluate kinematic self-similar perfect fluid and dust solutions for the most general cylindrically symmetric spacetime. We explore kinematic self-similar solutions of the first, second, zeroth and infinite kinds for parallel and orthogonal cases. It is found that the parallel case gives solutions for both perfect fluid and dust cases in all kinds except the zeroth kind of the...

In this paper, we design and analyze a new zeroth-order online algorithm, namely, the zeroth-order online alternating direction method of multipliers (ZOO-ADMM), which enjoys dual advantages of being gradient-free operation and employing the ADMM to accommodate complex structured regularizers. Compared to the first-order gradient-based online algorithm, we show that ZOO-ADMM requires √ m times ...

It is well known since the pioneering work of Goldbeter and Koshland [Proc. Natl. Acad. Sci. USA, vol. 78, pp. 6840-6844 (1981)] that cellular phosphorylationdephosphorylation cycle (PdPC), catalyzed by kinase and phosphatase under saturated condition with zeroth order enzyme kinetics, exhibits ultrasensitivity, sharp transition. We analyse the dynamics aspects of the zeroth order PdPC kinetics...

Abstract We establish a kind of ‘degree $0$ Freudenthal ${\mathbb {G}_m}$ -suspension theorem’ in motivic homotopy theory. From this we deduce results about the conservativity $\mathbb P^1$ -stabilization functor. In order to these results, show how compute certain pullbacks cohomology strictly homotopy-invariant sheaf terms Rost–Schmid complex. This establishes main conjecture [2], which easil...