Related papers: On Minimization of a Quadratic Binary Functional
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the…
Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
For many optimization problems in machine learning, finding an optimal solution is computationally intractable and we seek algorithms that perform well in practice. Since computational intractability often results from pathological…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational…
Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier…
Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…
To efficiently find an optimum parameter combination in a large-scale problem, it is a key to convert the parameters into available variables in actual machines. Specifically, quadratic unconstrained binary optimization problems are solved…
We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for…