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Found 22 papers, 1 papers with code
Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization
Preliminary numerical experiments on deep learning tasks illustrate that our proposed framework yields efficient variants of Lagrangian-based methods with convergence guarantees for nonconvex nonsmooth constrained optimization problems.
An Inexact Halpern Iteration with Application to Distributionally Robust Optimization
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties.
On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation.
Adam-family Methods with Decoupled Weight Decay in Deep Learning
As a practical application of our proposed framework, we propose a novel Adam-family method named Adam with Decoupled Weight Decay (AdamD), and establish its convergence properties under mild conditions.
Convergence Guarantees for Stochastic Subgradient Methods in Nonsmooth Nonconvex Optimization
In this paper, we investigate the convergence properties of the stochastic gradient descent (SGD) method and its variants, especially in training neural networks built from nonsmooth activation functions.
Nonconvex Stochastic Bregman Proximal Gradient Method with Application to Deep Learning
Experimental results on representative benchmarks demonstrate the effectiveness and robustness of MSBPG in training neural networks.
Adam-family Methods for Nonsmooth Optimization with Convergence Guarantees
In this paper, we present a comprehensive study on the convergence properties of Adam-family methods for nonsmooth optimization, especially in the training of nonsmooth neural networks.
Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant
We consider polynomial optimization problems (POP) on a semialgebraic set contained in the nonnegative orthant (every POP on a compact set can be put in this format by a simple translation of the origin).
Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decomposition
This work proposes a rapid algorithm, BM-Global, for nuclear-norm-regularized convex and low-rank matrix optimization problems.
An Inexact Projected Gradient Method with Rounding and Lifting by Nonlinear Programming for Solving Rank-One Semidefinite Relaxation of Polynomial Optimization
In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework.
Learning Graph Laplacian with MCP
We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP).
Estimation of sparse Gaussian graphical models with hidden clustering structure
The sparsity and clustering structure of the concentration matrix is enforced to reduce model complexity and describe inherent regularities.
Efficient algorithms for multivariate shape-constrained convex regression problems
We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points.
A sparse semismooth Newton based proximal majorization-minimization algorithm for nonconvex square-root-loss regression problems
In this paper, we consider high-dimensional nonconvex square-root-loss regression problems and introduce a proximal majorization-minimization (PMM) algorithm for these problems.
A dual Newton based preconditioned proximal point algorithm for exclusive lasso models
In addition, we derive the corresponding HS-Jacobian to the proximal mapping and analyze its structure --- which plays an essential role in the efficient computation of the PPA subproblem via applying a semismooth Newton method on its dual.
Convex Clustering: Model, Theoretical Guarantee and Efficient Algorithm
The perfect recovery properties of the convex clustering model with uniformly weighted all pairwise-differences regularization have been proved by Zhu et al. (2014) and Panahi et al. (2017).
A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters
When the support points of the barycenter are pre-specified, this problem can be modeled as a linear programming (LP) problem whose size can be extremely large.
Efficient sparse semismooth Newton methods for the clustered lasso problem
Based on the new formulation, we derive an efficient procedure for its computation.
An Efficient Semismooth Newton Based Algorithm for Convex Clustering
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications.
Max-Norm Optimization for Robust Matrix Recovery
This paper studies the matrix completion problem under arbitrary sampling schemes.
Simultaneous Clustering and Model Selection for Tensor Affinities
Estimating the number of clusters remains a difficult model selection problem.
Practical Matrix Completion and Corruption Recovery using Proximal Alternating Robust Subspace Minimization
Low-rank matrix completion is a problem of immense practical importance.
