Article

Global minimisation of nonconvex functions by generalising the mirror descent method
Summary: In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving …
zbmath arxiv
A hitchhiker's guide to first-order elliptic boundary value problems
Summary: To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user’s …
zbmath arxiv
A lower bound theorem for $d$-polytopes with $2d+2$ vertices
Summary: We establish a lower bound theorem for the number of $k$-faces ($1\le k\le d-2$) in a $d$-dimensional polytope $P$ …
zbmath arxiv
A lower bound theorem for $d$-polytopes with at most $3d-1$ vertices
zbmath arxiv
A refined lower bound theorem for $d$-polytopes with at most $2d$ vertices
zbmath arxiv
First-order elliptic boundary value problems on manifolds with non-compact boundary
Summary: We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, …
Cite DOI zbmath arxiv
Frank-Wolfe algorithm for DC optimization problem
zbmath arxiv
Frank-Wolfe algorithm for star-convex functions
Summary: We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact …
zbmath arxiv
Geometric singularities and Hodge theory
Summary: We consider smooth vector bundles over smooth manifolds equipped with non-smooth geometric data. For nilpotent differential …
zbmath arxiv
KKT-based optimality conditions for neural network approximation
Summary: In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in …
zbmath arxiv