相关论文: A proximal dual semismooth Newton method for compu…

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…

Reinforcement learning is widely used in applications where one needs to perform sequential decisions while interacting with the environment. The problem becomes more challenging when the decision requirement includes satisfying some safety…

We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian…

Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…

The low-rank matrix approximation problem with respect to the component-wise $\ell_1$-norm ($\ell_1$-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine…

The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they…

In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…

Solving the distributional worst-case in the distributionally robust optimization problem is equivalent to finding the projection onto the intersection of simplex and singly linear inequality constraint. This projection is a key component…

Recently, Musco and Woodruff (FOCS, 2017) showed that given an $n \times n$ positive semidefinite (PSD) matrix $A$, it is possible to compute a $(1+\epsilon)$-approximate relative-error low-rank approximation to $A$ by querying…

We develop R2N, a modified quasi-Newton method for minimizing the sum of a $\mathcal{C}^1$ function $f$ and a lower semi-continuous prox-bounded $h$. Both $f$ and $h$ may be nonconvex. At each iteration, our method computes a step by…

Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…

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…

We present a proximal quasi-Newton method in which the approximation of the Hessian has the special format of "identity minus rank one" (IMRO) in each iteration. The proposed structure enables us to effectively recover the proximal point.…

Low rank matrix approximation (LRMA), which aims to recover the underlying low rank matrix from its degraded observation, has a wide range of applications in computer vision. The latest LRMA methods resort to using the nuclear norm…

In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

The exclusive lasso (also known as elitist lasso) regularization has become popular recently due to its superior performance on group sparsity. Compared to the group lasso regularization which enforces the competition on variables among…

We consider the efficient minimization of a nonlinear, strictly convex functional with $\ell_1$-penalty term. Such minimization problems appear in a wide range of applications like Tikhonov regularization of (non)linear inverse problems…

The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to…

Mean-variance optimization (MVO) is known to be sensitive to estimation error in its inputs. Norm penalization of MVO programs is a regularization technique that can mitigate the adverse effects of estimation error. We augment the standard…