Related papers: Projected shrinkage algorithm for box-constrained …

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…

Bilevel optimization has been recently revisited for designing and analyzing algorithms in hyperparameter tuning and meta learning tasks. However, due to its nested structure, evaluating exact gradients for high-dimensional problems is…

This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…

The vast majority of real world classification problems are imbalanced, meaning there are far fewer data from the class of interest (the positive class) than from other classes. We propose two machine learning algorithms to handle highly…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…

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 propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…

In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…

Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

The l1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l1-norm minimization for quaternion signals by converting it to second-order…

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…

A plethora of recent research has focused on improving the memory footprint and inference speed of deep networks by reducing the complexity of (i) numerical representations (for example, by deterministic or stochastic quantization) and (ii)…

Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient…

Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…

We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…

We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…