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We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
We consider the distributed optimization problem in which a network of agents aims to minimize the average of local functions. To solve this problem, several algorithms have recently been proposed where agents perform various combinations…
In this paper, we consider the sparse least squares regression problem with probabilistic simplex constraint. Due to the probabilistic simplex constraint, one could not apply the L1 regularization to the considered regression model. To find…
A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…
We propose a First-Order System Least Squares (FOSLS) method based on deep-learning for numerically solving second-order elliptic PDEs. The method we propose is capable of dealing with either variational and non-variational problems, and…
We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from…
We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted…
Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…
Many practical problems can be formulated as l0-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative solutions to underdetermined linear systems. Recent study indicates that l1-minimization is efficient…
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…
We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator part is a…
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…
On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many…