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In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...
We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...
This paper is devoted to the study of the generalized impedance boundary conditions (GIBCs) for a strongly absorbing obstacle in the time regime in two and three dimensions. The GIBCs in the time domain are heuristically derived from the corresponding cond ...
We address the problem of minimizing a convex smooth function f(x) over a compact polyhedral set D given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as personalized medicin ...
We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The alg ...
Structured constraints in Machine Learning have recently brought the Frank-Wolfe (FW) family of algorithms back into the spotlight. While the classical FW algorithm has poor local convergence properties, Away-steps FW and Pairwise FW have emerged as improv ...
This thesis is a study of harmonic maps in two different settings. The first part is concerned with harmonic maps from smooth metric measure spaces to Riemannian manifolds. The second part is study of harmonic maps from Riemannian polyhedra to non-positive ...
