Related papers: An implicit algorithm for validated enclosures of …
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
Previous algorithms can solve convex-concave minimax problems $\min_{x \in \mathcal{X}} \max_{y \in \mathcal{Y}} f(x,y)$ with $\mathcal{O}(\epsilon^{-2/3})$ second-order oracle calls using Newton-type methods. This result has been…
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
We present a simple transformation of any linear program or semidefinite program into an equivalent convex optimization problem whose only constraints are linear equations. The objective function is defined on the whole space, making…
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves.…
In the Upper Degree-Constrained Partial Orientation problem we are given an undirected graph $G=(V,E)$, together with two degree constraint functions $d^-,d^+ : V \to \mathbb{N}$. The goal is to orient as many edges as possible, in such a…
The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…
This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…
We propose a numerical method based on physics-informed Random Projection Neural Networks for the solution of Initial Value Problems (IVPs) of Ordinary Differential Equations (ODEs) with a focus on stiff problems. We address an Extreme…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we…
Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization.…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of the ODE-nets using unrolled implicit schemes for ease of…
In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
In this work we propose a novel Hybrid High-Order method for the incompressible Navier--Stokes equations based on a formulation of the convective term including Temam's device for stability. The proposed method has several advantageous…
We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a…
The component-by-component (CBC) algorithm is a method for constructing good generating vectors for lattice rules for the efficient computation of high-dimensional integrals in the "weighted" function space setting introduced by Sloan and…