Related papers: On the Complexity of the Plantinga-Vegter Algorith…

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem - a set of target alignments, an associated…

In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate…

This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…

Continuous amortization is a technique for computing the complexity of algorithms, and it was first presented by the author in Burr, Krahmer, & Yap (2009). Continuous amortization can result in simpler and more straight-forward complexity…

We propose a general approach to compute the seed sensitivity, that can be applied to different definitions of seeds. It treats separately three components of the seed sensitivity problem -- a set of target alignments, an associated…

This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…

We introduce a novel machine learning method called the Penalized Profile Support Vector Machine based on the Gabriel edited set for the computation of the probability of failure for a complex system as determined by a threshold condition…

Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find…

Recent agent frameworks and inference-time algorithms often struggle with complex planning problems due to limitations in verifying generated plans or reasoning and varying complexity of instances within a single task. Many existing methods…

The Plant Propagation Algorithm, epitomised by the Strawberry Algorithm, has been previously successfully tested on low dimensional continuous optimisation problems. It is a neighborhood search algorithm. In this paper, we introduce, robust…

Let f be a univariate polynomial with real coefficients, f in R[X]. Subdivision algorithms based on algebraic techniques (e.g., Sturm or Descartes methods) are widely used for isolating the real roots of f in a given interval. In this…

We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…

This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…