Related papers: Solving large linear least squares problems with l…
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketched LS (sLS) problem, and use the solution of the sLS…
Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…
There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
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…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix…
In our work, we consider the linear least squares problem for $m\times n$-systems of linear equations $Ax = b$, $m\geq n$, such that the matrix $A$ and right-hand side vector $b$ can vary within an interval $m\times n$-matrix and an…
The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
We consider large-scale nonlinear least squares problems with sparse residuals, each of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…