Related papers: A Path Algorithm for Constrained Estimation

The estimation of a precision matrix is a crucial problem in various research fields, particularly when working with high dimensional data. In such settings, the most common approach is to use the penalized maximum likelihood. The…

Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones,…

Safe reinforcement learning aims to learn the optimal policy while satisfying safety constraints, which is essential in real-world applications. However, current algorithms still struggle for efficient policy updates with hard constraint…

In this article we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be…

SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many…

This work studies the multi-task functional linear regression models where both the covariates and the unknown regression coefficients (called slope functions) are curves. For slope function estimation, we employ penalized splines to…

We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. We prove convergence of our numerical method under reasonably mild assumptions: boundedness and…

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding…

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…

We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters…

Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…

Penalized regression is an attractive framework for variable selection problems. Often, variables possess a grouping structure, and the relevant selection problem is that of selecting groups, not individual variables. The group lasso has…

Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a…

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent…

We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the…

We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…

Extracting useful information from high-dimensional data is an important focus of today's statistical research and practice. Penalized loss function minimization has been shown to be effective for this task both theoretically and…

Challenges with data in the big-data era include (i) the dimension $p$ is often larger than the sample size $n$ (ii) outliers or contaminated points are frequently hidden and more difficult to detect. Challenge (i) renders most conventional…