The differentiability of Fourier gap series and“Riemann’s example” of a continuous, nondifferentiable function - Luther - 1986 () Citation Context ...e right hand side of (5.1) is differentiable for any x > 0. On the other hand, the second term on the right hand side of (5.1) is...
Das. "Characterization of non-differentiable points of a function by Fractional derivative of Jumarie type". European Journal of Academic Essays 2015; 2(2): 70-86. (2015).U. Ghosh, S. Sengupta, S. Sarkar and S. Das. Characterization of non-differentiable points of a function by ...
The fractal dimensions, D b and the multifractal singularity distribution functions, F ( α ) for Riemann's 'non-differentiable' functions are calculated numerically and presented here for the first time. The new fractal results are discussed through comparison with some analytically known properties ...
IPOPT assumes twice continuously differentiable objective function and constraints, which is not the case for the nonsmooth models. Furthermore, there are issues regarding the termination criteria. Specifically, no nonsmooth analog currently exists for the dual feasibility calculations in IPOPT, such that...
where f : Rn→ R is a nondifferentiable convex function. It is well known that many practical problems can be formulated as (1.1), for example the problem of catastrophe, ruin, vitality, data mining, and finance. A classical conceptual algorithm for solving (1.1) is the proximal point meth...
Is not differentiable at x = 0, however it is convex at that point. From point 3, we know that f has directional derivatives at x = 0. Obviously, if a function is differentiable we can define the gradient of f. For differentiable functions do not define the subgradient , which makes...
M is a compact, connected, orientable, differentiable n-manifold of class C, and f is a non-degenerate function of class C. This note reveals certain fundamental topological characteristics of M by combining the study of the critical points of f with the study of certain differentiable submanif...
[59]. Common specifications for the regularizing function are, or. In the first case, we obtainon, whereas in the second case, we get. Note that the first case yields the objectivefwhich is non-convex and non-differentiable at the boundary of the feasible set. It has been reported in ...
For differentiable functions, Antczak introduced the G-invexity in []. Note from Ex- ample that the function ϕ(f ) may be not differentiable even if the function ϕ is differen- tiable. Thus, it is necessary to introduce the following vector (Gf , βf )-invexity concept...
Alternating direction method of multipliers (ADMM) is a widely used algorithm for solving two-block separable problems with linear constraints. However, its applicability in various fields is limited by the need to assume the global Lipschitz continuity of the gradient of di...