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We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local…

One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…

We describe a new library named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (e.g., sparse linear regression, sparse logistic regression, sparse Poisson…

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the…

In this paper, we propose a novel variable-separation (NVS) method for generic multivariate functions. The idea of NVS is extended to to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs).…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…

This is an overview paper written in style of research proposal. In recent years we introduced a general framework for large-scale unconstrained optimization -- Sequential Subspace Optimization (SESOP) and demonstrated its usefulness for…

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as…

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite…

Partial Least Squares (PLS) regression emerged as an alternative to ordinary least squares for addressing multicollinearity in a wide range of scientific applications. As multidimensional tensor data is becoming more widespread, tensor…

Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to…

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Sparse tensor decomposition and completion are common in numerous applications, ranging from machine learning to computational quantum chemistry. Typically, the main bottleneck in optimization of these models are contractions of a single…

This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under…

We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization…

Side information provides a pivotal role for message delivery in many communication scenarios to accommodate increasingly large data sets, e.g., caching networks. Although index coding provides a fundamental modeling framework to exploit…

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…