Related papers: Greedy permanent magnet optimization
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Resource scheduling is critical in many industries, especially in power systems. The Unit Commitment problem determines the on/off status and output levels of generators under many constraints. Traditional exact methods, such as…
The taxing computational effort that is involved in solving some high-dimensional statistical problems, in particular problems involving non-convex optimization, has popularized the development and analysis of algorithms that run…
Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Since a distributive lattice is used to represent a dependency constraint, the problem can…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items…
We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized…
In this paper two formulations for the robust optimization of the size of the permanent magnet in a synchronous machine are discussed. The optimization is constrained by a partial differential equation to describe the electromagnetic…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…