Related papers: Greedy approximation in convex optimization
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach…
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…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
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…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…
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…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Sparse matrices are favorable objects in machine learning and optimization. When such matrices are used, in place of dense ones, the overall complexity requirements in optimization can be significantly reduced in practice, both in terms of…
Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
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…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
When developing robust preconditioners for multiphysics problems, fractional functions of the Laplace operator often arise and need to be inverted. Rational approximation in the uniform norm can be used to convert inverting those fractional…
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…
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies.…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…