14 papers
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,…
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…
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…
An abstract effective convergence theorem for stochastic processes, with applications to stochastic approximation
Morenikeji Neri, Nicholas Pischke, Thomas Powell
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is tha…
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 constr…