A readily implementable algorithm is given for minimizing any convex, not necessarily differentiable, function/of several variables. At each iteration the method requires only one approximate evaluation of /and its E-subgradient, and finds a search direction by solving a small quadratic programming problem. The algorithm generates a minimizing sequence of points, which converges to a solution w...

In this paper we consider general Hadamard differentiable functionals φ(ΛR,ΛT ) of the cumulative hazard functions of two samples of randomly right censored data, which can be used for the nonparametric assessment of noninferiority. We prove the consistency of various bootstrap procedures as suggested in Freitag et al. [1] for the practical implementation of tests for this problem.

Artificial reverberation (AR) models play a central role in various audio applications. Therefore, estimating the AR model parameters (ARPs) of reference is crucial task. Although few recent deep-learning-based approaches have shown promising performance, their non-end-to-end training scheme prevents them from fully exploiting potential deep neural networks. This motivates introduction differen...

It should be evident to you that (1.5) is equivalent to (1.3). Visually, if the graph of a function f at (a, f(a)) either has no unique tangent line or has a vertical tangent line then f is not differentiable at the point a. A function that is differentiable at every point in Dom(f) is said to be differentiable. A function that is differentiable at every point in a set S ⊂ Dom(f) is said to be ...

The domain (δ) of a closed ∗-derivation δ in C(K) (K : a compact Hausdorff space) is a generalization of the space C(1)[0,1] of differentiable functions on [0,1]. In this paper, a problem proposed by Jarosz (1985) is studied in the context of derivations instead of C(1)[0,1].

In this paper, we prove a Halpern-type strong convergence theorem for nonexpansive mappings in a Banach space whose norm is uniformly Gâteaux differentiable. Also, we discuss the sufficient and necessary condition about this theorem. This is a partial answer of the problem raised by Reich in 1983.

Let F be a nonlinear Fréchet differentiable map in a real Hilbert space. Condition sufficient for existence of a solution to the equation F (u) = 0 is given, and a method (dynamical systems method, DSM) to calculate the solution as the limit of the solution to a Cauchy problem is justified under suitable assumptions.

Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The controlto-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly...

Data imputation has been extensively explored to solve the missing data problem. The dramatically increasing volume of incomplete makes models computationally infeasible in many real-life applications. In this paper, we propose an effective scalable system named SCIS significantly speed up training differentiable generative adversarial under accuracy-guarantees for large-scale data. consists tw...