This study presents a new approach for optimal allocation of distributed generation (DG) and energy storage system (ESS) in microgrids (MGs). The practical optimal allocation problems have non-smooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A dynamic capacity adjustment algorithm is i...

We prove that, for general cost functions on R, or for the cost d/2 on a Riemannian manifold, optimal transport maps between smooth densities are always smooth outside a closed singular set of measure zero.

The performance of online convex optimization algorithms in a dynamic environment is often expressed terms the regret, which measures decision maker’s against sequence time-varying comparators. In analysis prior works assume Lipschitz continuity or uniform smoothness cost functions. However, there are many important functions practice that do not satisfy these conditions. such cases, analyses a...

We discuss a bundle method for non-smooth non-convex optimization programs. In the absence of convexity, a substitute for the cutting plane mechanism has to be found. We propose such a mechanism and prove convergence of our method in the sense that every accumulation point of the sequence of serious iterates is critical.

This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity-based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp ...

Techniques of interval extensions and interval Newton methods have been developed for verified solution of nonlinear systems of equations and for global optimization. In most of the literature to date, such interval extensions and interval Newton methods are applicable when the functions are given by smooth expressions, without conditional branches. In fact, however, many practical problems, in...