相关论文: A Screening Strategy for Structured Optimization I…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Iteratively reweighted L1 (IRL1) algorithm is a common algorithm for solving sparse optimization problems with nonconvex and nonsmooth regularization. The development of its acceleration algorithm, often employing Nesterov acceleration, has…
Regularizing neural networks is important for anticipating model behavior in regions of the data space that are not well represented. In this work, we propose a regularization technique for enforcing a level of smoothness in the mapping…
This paper primarily focuses on computing the Euclidean projection of a vector onto the $\ell_{p}$ ball in which $p\in(0,1)$. Such a problem emerges as the core building block in statistical machine learning and signal processing tasks…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…
We consider the problem of minimizing an objective function that is the sum of a convex function and a group sparsity-inducing regularizer. Problems that integrate such regularizers arise in modern machine learning applications, often for…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Parameter pruning is a promising approach for CNN compression and acceleration by eliminating redundant model parameters with tolerable performance loss. Despite its effectiveness, existing regularization-based parameter pruning methods…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…