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Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
We propose an algorithm for determining the irreducible polynomials over finite fields, based on the use of the companion matrix of polynomials and the generalized Jordan normal form of square matrices.
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
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 present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We develop a simple and efficient algorithm for approximating the John Ellipsoid of a symmetric polytope. Our algorithm is near optimal in the sense that our time complexity matches the current best verification algorithm. We also provide…
In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…
Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning. Current machine learning methods, however, struggle to solve Olympiad-level problems beyond Euclidean plane…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
We consider multicriteria problems of evaluating absolute ratings (scores, priorities, weights) of given alternatives for making decisions, which are compared in pairs under several criteria. Given matrices of pairwise comparisons of…
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…
The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…
Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
Algorithmic fairness has been framed as a newly emerging technology that mitigates systemic discrimination in automated decision-making, providing opportunities to improve fairness in information systems (IS). However, based on a…