Related papers: Solving Laplace problems with the AAA algorithm
We extend Random Access, a fundamental operation that enables efficient search and exploration algorithms, to the modern interactive data systems based on Ranked Retrieval and Similarity Search, where orderings are dynamically defined over…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
In this paper, we aim at unifying, simplifying and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central…
In this article we propose a shooting algorithm for optimal control problems governed by systems that are affine in one part of the control variable. Finitely many equality constraints on the initial and final state are considered. We…
Optimization problems in design engineering are complex by nature, often because of the involvement of critical objective functions accompanied by a number of rigid constraints associated with the products involved. One such problem is…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
This paper presents a novel backtracking strategy for additive Schwarz methods for general convex optimization problems as an acceleration scheme. The proposed backtracking strategy is independent of local solvers, so that it can be applied…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
Agility Assessment (AA) comprises tools, assessment techniques, and frameworks that focus on indicating how a company or a team is applying agile techniques and eventually pointing out problems in adopting agile practices at a…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the…
In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Uncertainty quantification for deep neural networks has recently evolved through many techniques. In this work, we revisit Laplace approximation, a classical approach for posterior approximation that is computationally attractive. However,…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
We study the accuracy of a class of methods to compute the Inverse Laplace Transform, the so-called \emph{Abate--Whitt methods} [Abate, Whitt 2006], which are based on a linear combination of evaluations of $\widehat{f}$ in a few points. We…
Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations…