The Boosted Double-Proximal Subgradient Algorithm for Nonconvex Optimization

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of composite functions. BDSA exploits the combined nature of subgradients from the data and proximal steps, and integrates a line-search procedure to enhance its performance. While BDSA encompasses existing schemes proposed in the literature, it extends its applicability to more diverse problem domains. We establish the convergence of BDSA under the Kurdyka--Lojasiewicz property and provide an analysis of its convergence rate. To evaluate the effectiveness of BDSA, we introduce a novel family of challenging test functions with an abundance of critical points. We conduct comparative evaluations demonstrating its ability to effectively escape non-optimal critical points. Additionally, we present two practical applications of BDSA for testing its efficacy, namely, a constrained minimum-sum-of-squares clustering problem and a nonconvex generalization of Heron's problem

A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting

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. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.FJAA and DTB were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22. FJAA was partially supported by the Generalitat Valenciana (AICO/2021/165). RIB was partially supported by FWF (Austrian Science Fund), project P 34922-N. DTB was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.The work of Yair Censor was supported by the ISF-NSFC joint research plan Grant Number 2874/19. Francisco Aragón and David Torregrosa were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and the Generalitat Valenciana (AICO/2021/165). David Torregrosa was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.Comment: Revised version, October 10, 2022; accepted for publication in: Applied Mathematics and Computatio

Distributed Forward-Backward Methods for Ring Networks

In this work, we propose and analyse forward-backward-type algorithms for finding a zero of the sum of finitely many monotone operators, which are not based on reduction to a two operator inclusion in the product space. Each iteration of the studied algorithms requires one resolvent evaluation per set-valued operator, one forward evaluation per cocoercive operator, and two forward evaluations per monotone operator. Unlike existing methods, the structure of the proposed algorithms are suitable for distributed, decentralised implementation in ring networks without needing global summation to enforce consensus between nodes.Comment: 19 page

Metodologías colaborativas a través de las tecnologías: hacia una evaluación equitativa.

Presentación de buenas prácticas metodológicas en el área de tecnología educativa, transferidas por el Grupo de investigación consolidado GTEA, Universidad de Málaga (SEJ-462

Representaciones conformes de superficies de CURVATURA GAUSSIANA o curvatura media constante en 3-variedades

Conformal representations provide a way of describing a surface by holomorphic data. The origin of this representations was given by the Weierstrass-Enneper representation for minimal surfaces in ℝ3 which entailed a great development of the theory of this surfaces in the XIX century. In this work we study the Weierstrass-Enneper representation, the conformal representation of constant mean curvature one surfaces (Bryant surfaces) and null Gaussian curvature surfaces (at surfaces) in ℍ3 , and the interrelation between these three.Las representaciones conformes permiten describir una superficie por medio de datos holomorfos. El origen de estas representaciones tuvo lugar con la Representación de Weierstrass-Enneper para superficies mínimas en ℝ3 que supuso un gran desarrollo en la teoría de estas superficies en el siglo XIX. En este trabajo estudiaremos la representación de Weierstrass-Enneper, la representación conforme de superficies de curvatura media constante 1 (superficies de Bryant) y superficies de curvatura Gaussiana 0 (superficies llanas) en ℍ3 , y las relaciones entre ellasUniversidad de Sevilla. Máster Universitario en Matemática

A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes

This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25(4), 829–858, 2017) for computing a zero of the sum of three maximally monotone operators, with one of them being cocoercive. We provide a direct proof that guarantees its convergence when the stepsizes are smaller than four times the cocoercivity constant, thus doubling the size of the interval established by Davis and Yin. As a by-product, the same conclusion applies to the forward-backward splitting algorithm. Further, we use the notion of “strengthening” of a set-valued operator to derive a new splitting algorithm for computing the resolvent of the sum. Last but not least, we provide some numerical experiments illustrating the importance of appropriately choosing the stepsize and relaxation parameters of the algorithms.FJAA and DTB were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22. FJAA was partially supported by the Generalitat Valenciana (AICO/2021/165). DTB was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Patient-Level, Institutional, and Temporal Variations in Use of Imaging Modalities to Confirm Pulmonary Embolism

International audienceBackground: The choice of the imaging modality for diagnosis of pulmonary embolism (PE) could be influenced by provider, patient or hospital characteristics, or over time. However, little is known about the choice of the diagnostic modalities in practice. The aim of this study was to evaluate the variations in the use of imaging modalities for patients with acute PE. Methods: Using the data from Registro Informatizado Enfermedad TromboEmbolica (RIETE), a prospective international registry of patients with venous thromboembolism (March 2001–January 2019), we explored the imaging modalities used in patients with acute PE. The imaging modalities included computed tomography pulmonary angiography, ventilation/perfusion scanning, pulmonary angiography, a combination of these tests, or PE signs and symptoms plus imaging-confirmed proximal deep vein thrombosis but no chest imaging. Results: Among 38 025 patients with confirmed PE (53.1% female, age: 67.3±17 years), computed tomography pulmonary angiography was the dominant modality of diagnosis in all RIETE enrollees (78.2% [99% CI, 77.6–78.7]); including pregnant patients (58.9% [99% CI, 47.7%–69.4%]) and patients with severe renal insufficiency (62.5% [99% CI, 59.9–65.0]). A greater proportion of patients underwent ventilation/perfusion scanning in larger hospitals compared with smaller hospitals (13.1% versus 7.3%, P <0.001). The use of computed tomography pulmonary angiography varied between 13.3% and 98.3% across the countries, and its use increased over time (46.5% in 2002 to 91.7% in 2018, P <0.001). Conclusions: In a large multinational PE registry, variations were observed in the use of imaging modalities according to patient or institutional factors and over time. However, computed tomography pulmonary angiography was the dominant modality of diagnosis, even in pregnancy and severe renal insufficiency. The safety, costs, and downstream effects of these tests on PE-related and non-PE-related outcomes warrant further investigation