Related papers: The Complexity of Primal-Dual Fixed Point Methods …
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive…
We consider simple bilevel optimization problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i)…
We study the minmax optimization problem introduced in [22] for computing policies for batch mode reinforcement learning in a deterministic setting. First, we show that this problem is NP-hard. In the two-stage case, we provide two…
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this…
In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…
Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables.…
There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…
We consider the problem of classification of functional data into two groups by linear classifiers based on one-dimensional projections of functions. We reformulate the task to find the best classifier as an optimization problem and solve…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing…
Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…
Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…