Related papers: Scalable First-order Method for Certifying Optimal…
First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…
We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this paper we develop efficient first-order algorithms for the generalized trust-region subproblem (GTRS), which has applications in signal processing, compressed sensing, and engineering. Although the GTRS, as stated, is nonlinear and…
We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we…
This work provides the first finite-time convergence guarantees for linearly constrained stochastic bilevel optimization using only first-order methods, requiring solely gradient information without any Hessian computations or second-order…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
Portfolio optimization involves selecting asset weights to minimize a risk-reward objective, such as the portfolio variance in the classical minimum-variance framework. Sparse portfolio selection extends this by imposing a cardinality…
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
The problem of optimal precision switching for the conjugate gradient (CG) method applied to sparse linear systems is considered. A sparse matrix is defined as an $n\!\times\!n$ matrix with $m\!=\!O(n)$ nonzero entries. The algorithm first…