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Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…
The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is…
We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…
Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection,…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
Classification and probability estimation are fundamental tasks with broad applications across modern machine learning and data science, spanning fields such as biology, medicine, engineering, and computer science. Recent development of…