Related papers: Sparse-BSOS: a bounded degree SOS hierarchy for la…
This paper develops column partition based distributed schemes for a class of large-scale convex sparse optimization problems, e.g., basis pursuit (BP), LASSO, basis pursuit denosing (BPDN), and their extensions, e.g., fused LASSO. We are…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…
Global optimization has gained attraction over the past decades, thanks to the development of both theoretical foundations and efficient numerical routines. Among recent advances, Kernel Sum of Squares (KernelSOS) provides a powerful…
The moment sum of squares (moment-SOS) hierarchy produces sequences of upper and lower bounds on functionals of the exit time solution of a polynomial stochastic differential equation with polynomial constraints, at the price of solving…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
Stochastic zeroth-order (SZO), or gradient-free, optimization allows to optimize arbitrary functions by relying only on function evaluations under parameter perturbations, however, the iteration complexity of SZO methods suffers a factor…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
Demixing problems in many areas such as hyperspectral imaging and differential optical absorption spectroscopy (DOAS) often require finding sparse nonnegative linear combinations of dictionary elements that match observed data. We show how…
We consider the problem of sparse atomic optimization, where the notion of "sparsity" is generalized to meaning some linear combination of few atoms. The definition of atomic set is very broad; popular examples include the standard basis,…
We address the challenge of zeroth-order online convex optimization where the objective function's gradient exhibits sparsity, indicating that only a small number of dimensions possess non-zero gradients. Our aim is to leverage this…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…
Modern large scale machine learning applications require stochastic optimization algorithms to be implemented on distributed computational architectures. A key bottleneck is the communication overhead for exchanging information such as…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems.…
Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and could accelerate optimization algorithms for solving large scale convex optimization problems with…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squares (SOS) programming. We exploit the sparsity of the…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…