Related papers: Sparse Approximations with Interior Point Methods
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…
A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
We propose an efficient optimization algorithm for selecting a subset of training data to induce sparsity for Gaussian process regression. The algorithm estimates an inducing set and the hyperparameters using a single objective, either the…
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…
In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth…
This paper delves into stochastic optimization problems that involve Markovian noise. We present a unified approach for the theoretical analysis of first-order gradient methods for stochastic optimization and variational inequalities. Our…
Sparse Gaussian Processes are a key component of high-throughput Bayesian Optimisation (BO) loops; however, we show that existing methods for allocating their inducing points severely hamper optimisation performance. By exploiting the…
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…
It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…
In post--layout circuit simulation, efficient model order reduction (MOR) for many--port resistor--capacitor (RC) circuits remains a crucial issue. The current mainstream MOR methods for such circuits include high--order moment matching…
Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…
In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…