We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algori...

Abstract Variational regularization techniques are dominant in the field of mathematical imaging. A drawback these is that they dependent on a number parameters which have to be set by user. by-now common strategy resolve this issue learn from data. While mathematically appealing, leads nested optimization problem (known as bilevel optimization) computationally very difficult handle. It when so...

Recent advances in derivative-free optimization allow efficient approximation of the global-optimal solutions sophisticated functions, such as functions with many local optima, non-differentiable and non-continuous functions. This article describes ZOOpt (Zeroth Order Optimization) toolbox that provides solvers is designed easy to use. single-machine parallel on basis python core multi-machine ...

We consider the optimization problem of minimizing R Ω G(|∇u|) + λχ{u>0} dx in the class of functions W (Ω) with u − φ0 ∈ W 1,G 0 (Ω), for a given φ0 ≥ 0 and bounded. W (Ω) is the class of weakly differentiable functions with R Ω G(|∇u|) dx < ∞. The conditions on the function G allow for a different behavior at 0 and at ∞. We prove that every solution u is locally Lipschitz continuous, that it ...