Related papers: The Discrete Dantzig Selector: Estimating Sparse L…
This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, $\ell_q$ Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation…
This work attempts to combine the strengths of two major technologies that have matured over the last three decades: global mixed-integer nonlinear optimization and branch-and-price. We consider a class of generally nonconvex mixed-integer…
This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum…
This work proposes a novel multi-objective optimization approach that globally finds a representative non-inferior set of solutions, also known as Pareto-optimal solutions, by automatically formulating and solving a sequence of weighted sum…
Cutting planes are crucial for the performance of branch-and-cut algorithms for solving mixed-integer programming (MIP) problems, and linear row aggregation has been successfully applied to better leverage the potential of several major…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
We propose Intermediate Layer Optimization (ILO), a novel optimization algorithm for solving inverse problems with deep generative models. Instead of optimizing only over the initial latent code, we progressively change the input layer…
We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm. We first prove that the…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
The minimax excess risk optimization (MERO) problem is a new variation of the traditional distributionally robust optimization (DRO) problem, which achieves uniformly low regret across all test distributions under suitable conditions. In…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
We study the problem of choosing the best subset of p features in linear regression given n observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
In the paper, we proposed the Dantzig selector based on the $\ell_{1}-\alpha \ell_{2}$~$(0< \alpha \leq1)$ minimization for the signal recovery. In the Dantzig selector, the constraint $\|{\bf A}^{\top}({\bf b}-{\bf A}{\bf x})\|_\infty \leq…
We focus on the high dimensional linear regression $Y\sim\mathcal{N}(X\beta^{*},\sigma^{2}I_{n})$, where $\beta^{*}\in\mathds{R}^{p}$ is the parameter of interest. In this setting, several estimators such as the LASSO and the Dantzig…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter…