Related papers: On computing sparse universal solvers for key prob…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In…
The total least squares problem with the general Tikhonov regularization can be reformulated as a one-dimensional parametric minimization problem (PM), where each parameterized function evaluation corresponds to solving an n-dimensional…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the…
In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…
In this work, we propose a novel discrete-time distributed algorithm for finding least-squares solutions of linear algebraic equations with a scheduling protocol to further enhance its scalability. Each agent in the network is assumed to…
As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems…
The main challenge of nonconvex optimization is to find a global optimum, or at least to avoid ``bad'' local minima and meaningless stationary points. We study here the extent to which algorithms, as opposed to optimization models and…
Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence.…
We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the…
The problem of finding a zero of the sum of two maximally monotone operators is of central importance in optimization. One successful method to find such a zero is the Douglas-Rachford algorithm which iterates a firmly nonexpansive operator…
Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
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,…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…