Let Ψ = {ψ1, . . . , ψL} ⊂ L2 := L2(−∞,∞) generate a tight affine frame with dilation factor M , where 2 ≤M ∈ Z, and sampling constant b = 1 (for the zeroth scale level). Then for 1 ≤ N ∈ Z, N×oversampling (or oversampling by N) means replacing the sampling constant 1 by 1/N . The Second Oversampling Theorem asserts that N×oversampling of the given tight affine frame generated by Ψ preserves a ...

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...

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 ...