This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation nonlinear coefficient in the principal part that locally Lipschitz continuous and directionally but not G\^ateaux differentiable. leads to control-to-state operator differentiable as well. Based on suitable regularization scheme, we derive C- strong stationarity conditions. Under additi...

In this paper, we consider a class of structured fractional minimization problems where the numerator part objective is sum convex function and Lipschitz differentiable (possibly) nonconvex function, while denominator function. By exploiting structure problem, propose first-order algorithm, namely, proximal-gradient-subgradient algorithm with backtracked extrapolation (PGSA_BE) for solving type...

Procedural modeling allows for an automatic generation of large amounts similar assets, but there is limited control over the generated output. We address this problem by introducing Automatic Differentiable Modeling (ADPM). The forward procedural model generates a final editable model. user modifies output interactively, and modifications are transferred back to as its parameters solving inver...

Marshal Ash [3] introduced the concept of (σ, τ) differentiable functions and studied the Riemann generalized derivatives In this article we study the convexity and monotonicity of (σ, τ) differentiable functions, using results by Hincin, Humke and Laczkovich, and using the Riemann generalized derivative. We give conditions such that the classic properties of differentiable functions hold also ...

and Applied Analysis 3 2. Proof of Theorems Consider the more general semilinear elliptic problem −Δu f x, u , in Ω, u > 0, in Ω, u 0, on ∂Ω, 2.1 where the function f x, s is locally Hölder continuous in Ω × 0,∞ and continuously differentiable with respect to the variable s. A function u is called to be a subsolution of problem 2.1 if u ∈ C2 Ω ∩ C Ω , and −Δu ≤ fx, u, in Ω, u > 0, in Ω, u 0, on...

In this paper, we study the link capacity assignment problem in packet-switched networks (CA problem) focusing on the case where link cost function is a piecewise linear concave function. This type of cost function arises in many communication network design problems such as those arising from developments in communication transmission technologies. It is already known that the method of link s...

The secant method is the most used iterative to solve an operator equation where involved nondifferentiable. A known problem that arises when applying this its accessibility. Then, we try improve it by using technique of decomposition involved, so in turn sum two operators, one differentiable and other continuous but not differentiable. For this, use a family Newton-secant-type methods from New...

2. , Functions differentiable on the boundaries of regions, Ann. of Math. vol. 35 (1934) pp. 482-fôS. 3. , Differentiable manifolds, Ann. of Math. vol. 37 (1936) pp. 645-680. 4. f Differentiable functions defined in arbitrary subsets of Euclidean space, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 309-317. Further references are given here. 5. H. O. Hirschfeld, Continuation of differentiable func...