7 citations · 28 across the 26 of their papers we have counts for
28 papers
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…
Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
Nicholas Pischke
We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear Hadamard spaces for approximating zeros of the mean of a stochastically perturbed…
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…
On the proximal point algorithm for strongly quasiconvex functions in Hadamard spaces
Nicholas Pischke
We prove the convergence of the proximal point algorithm for finding the unique minimizer of a strongly quasiconvex function in general nonlinear Hadamard spaces, generalizing a re…
Asymptotic regularity of a generalised stochastic Halpern scheme
Nicholas Pischke, Thomas Powell
We provide abstract, general and highly uniform rates of asymptotic regularity for a generalized stochastic Halpern-style iteration, which incorporates a second mapping in the styl…
Proof mining and probability theory
Morenikeji Neri, Nicholas Pischke
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima f…
Generalized Fejér monotone sequences and their finitary content
Nicholas Pischke
We provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of \emph{generalized Fejér monotonicity} where (…
Rates of convergence for the asymptotic behavior of second-order Cauchy problems
Nicholas Pischke
We provide a quantitative version of a result due to Poffald and Reich on the asymptotic behavior of solutions of a second-order Cauchy problem generated by an accretive operator i…
A proof-theoretic metatheorem for nonlinear semigroups generated by an accretive operator and applications
Nicholas Pischke
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-com…
On computational properties of Cauchy problems generated by accretive operators
Pedro Pinto, Nicholas Pischke
In this paper, we provide quantitative versions of results on the asymptotic behavior of nonlinear semigroups generated by an accretive operator due to O. Nevanlinna and S. Reich a…
Logical metatheorems for accretive and (generalized) monotone set-valued operators
Nicholas Pischke
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This…
Quantitative results on algorithms for zeros of differences of monotone operators in Hilbert space
Nicholas Pischke
We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm…
Quantitative analysis of a subgradient-type method for equilibrium problems
Nicholas Pischke, Ulrich Kohlenbach
We use techniques originating from the subdiscipline of mathematical logic called `proof mining' to provide rates of metastability and - under a metric regularity assumption - rate…
On Intermediate Justification Logics
Nicholas Pischke
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logi…
Standard Gödel modal logics are not realized by Gödel justification logics
Nicholas Pischke
We show that the standard Gödel modal logics, as initially introduced by Caicedo and Rodriguez in \cite{CR2009,CR2010}, are not realized by the basic Gödel justification logics alt…