7 citations · 28 across the 26 of their papers we have counts for
10 papers · 1 filter
Strong laws, random monotone vector fields and gradient flows on metric spaces of nonpositive curvature
Nicholas Pischke
Using a novel effective non-asymptotic concentration inequality, we establish a distribution-uniform generalization of Sturm's strong law of large numbers for inductive means of $L…
A relaxed-inertial proximal point algorithm for strongly quasiconvex equilibrium problems on Hadamard manifolds
Luisa Marie Després, Nicholas Pischke
We study a proximal point type method for approximating solutions to equilibrium problems generated by pseudomonotone and strongly quasiconvex bifunctions over Hadamard manifolds,…
On strongly quasiconvex pseudomonotone equilibrium problems in Hadamard spaces
Luisa Marie Després, Nicholas Pischke
We study two proximal point type methods for finding equilibrium points of pseudomonotone and strongly quasiconvex bifunctions. Extending results by A. Iusem and F. Lara, we prove…
Avoiding logical strength in real analysis
Anton Freund, Nicholas Pischke, Patrick Uftring
In reverse mathematics, real numbers are traditionally represented by Cauchy sequences with a given rate of convergence. We work without rates and speak of slow Cauchy sequences. I…
Convergence guarantees for stochastic algorithms solving non-unique problems in metric spaces
Nicholas Pischke, Thomas Powell
We prove a general quantitative theorem on the asymptotic behavior of stochastic quasi-Fejér monotone sequences in a broad metric context. Concretely, our result explicitly constru…
Weak convergence of the stochastic proximal point method in metric spaces
Nicholas Pischke
We prove the almost sure weak convergence of a stochastic proximal point method for minimizing a convex integral function in the general nonlinear context of complete geodesic metr…
A systematic way of analysing proofs in probability theory
Morenikeji Neri, Paulo Oliva, Nicholas Pischke
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of pr…
Effective rates for continuous-time quasi-Fejér monotone dynamical systems
Anton Freund, Nicholas Pischke
We provide quantitative convergence results for continuous-time dynamical systems in metric spaces that satisfy a continuous-time analog of quasi-Fejér monotonicity. More precisely…
Generalized fluctuation bounds for stochastic algorithms in the presence of compactness
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a convergence result for sequences of random variables taking values in a metric space that satisfy a stochastic quasi-Fejér monotonicity condition, in the context of a…
On Busemann subgradient methods for stochastic minimization in Hadamard spaces
Nicholas Pischke
We study the recently introduced Busemann subgradient method due to Goodwin, Lewis, López-Acedo and Nicolae, extending it to minimize the mean of a stochastic function over general…