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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…
Quantum machine learning models are designed for performing learning tasks. Some quantum classifier models are proposed to assign classes of inputs based on fidelity measurements. Quantum Hadamard test is a well-known quantum algorithm for…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We hereby introduce and study an algorithm able to search for initial conditions corresponding to orbits presenting forced oscillations terms only, namely to completely remove the free or proper oscillating part. This algorithm is based on…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
We consider potential games with mixed-integer variables, for which we propose two distributed, proximal-like equilibrium seeking algorithms. Specifically, we focus on two scenarios: i) the underlying game is generalized ordinal and the…
We consider the problem of minimizing a proper, lower semicontinuous, geodesically convex function on a Hadamard manifold. Building on ball-proximal (broximal) ideas in the Euclidean setting, viewed as an abstract proximal-type algorithm,…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…
The standard simplex in R^n, also known as the probability simplex, is the set of nonnegative vectors whose entries sum up to 1. They frequently appear as constraints in optimization problems that arise in machine learning, statistics, data…
Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
Given a dissimilarity matrix, the metric nearness problem is to find the nearest matrix of distances that satisfy the triangle inequalities. This problem has wide applications, such as sensor networks, image processing, and so on. But it is…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…
Inverse problems are common and important in many applications in computational physics but are inherently ill-posed with many possible model parameters resulting in satisfactory results in the observation space. When solving the inverse…