graduation at Matemática Aplicada e Computacional from Universidade Estadual de Campinas (2003), graduation at Licenciatura em Matemática from Universidade Estadual de Campinas (2006), master's at Mathematics from Universidade Estadual de Campinas (2005) and doctorate at Mathematics from Universidade Estadual de Campinas (2009). Has experience in Mathematics, focusing on Optimization, acting on the following subjects: Nonlinear Optimization, Conic Optimization, Numerical Analysis, Optimality Conditions, Algorithms, Applications. (Source: Lattes Curriculum)
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This project deals with theoretical, computational and application aspects of Optimization. The project aims at the development, theoretical analysis, implementation and application of algorithms for different aspects of Optimization, with emphasis on Continuous Optimization. The project relies on applications with which the team is familiar. Emphasis is placed on algorithms with a solid …
This proposal deals with practical algorithms for continuous optimization problems in a very general context known as nonlinear conic programming. This framework encompasses some well-established research fields in continuous optimization, such as nonlinear programming, nonlinear second-order cone programming, and nonlinear semidefinite programming. Each of these fields carry countless ap…
Our group has been active in the Brazilian scientific environment for 40 years, being is sensitive to new trends and modern applications of Optimization. Over the years, this group, funded by successive FAPESP thematic projects, has made significant contributions in areas involving decomposition methods, quasi-Newton methods, sequential quadratic programming, augmented Lagrangian methods,…
In this project we present several lines of research on the use of second-order information in nonlinear programming problems. Being second-order optimality conditions more accurate with respect to optimality than its first-order counterparts, the advantages of a second-order algorithm is evident, given those recent applications of nonlinear programming where guaranteeing optimality is pa…
(Only some records are available in English at this moment)
Recent developments in the field of conic optimization have addressed various open questions. In particular, a reduction strategy was employed to handle situations where the constraint is not located at the vertex of the cone. In this project, we aim to propose a reduction-free manner to formulate this condition. Additionally, we intend to investigate all known applications of constant ra…
Recently, the Euclidean circumcenter technique has been employed in order to introduce circumcentered-reflection methods (CRM) for solving convex feasibility problems (CFP). The cir-cumcenter technique is simple yet an effective way of accelerating usual optimization algorithms.Since then, circumcenter-oriented optimization algorithms have been thoroughly analyzed in the setting of Euclid…
An important class of constrained optimization problems that has recently received attention is the class of nonlinear conic programming problems. This class of problems is difficult to solve. For this reason, it can only be obtained solution candidates in practice. Despite this, it has been observed that when optimization problems are treated naturally, optimization algorithms have a bet…
The main objective of scientific initiation is the implementation of an Alternating Direction Method of Multipliers (ADMM) approach to solve the covariance matrix decomposition problem and explore its applications in various fields of economics.To apply ADMM to the covariance matrix decomposition problem, it is necessary for the matrix to be positive semidefinite (SDP), which is not alway…
The objective of this work is to develop an augmented Lagrangian-based method for finding a solution point for the two-player Nash equilibrium prioblem. In the literature, the methods for this kind of problem use the optimality conditions theory for finding stationary points via the Karush-Kuhn-Tucker (KKT) conditions, with the aid of some qualification constraint. Although these conditio…
This research project aims to extend the approximate KKT sequential condition for the context of nonlinear symmetric cone programming. For this purpose, an appropriate definition of the optimality condition is necessary so that it holds in a local minimizer without the need to require a qualification condition. In addition, such a condition must be satisfied by limit points of algorithms …
(Only some records are available in English at this moment)
This project focuses on addressing mathematical programming problems in Hilbert spaces using a safeguarded augmented Lagrangian method. Our proposal aims to achieve both practical and theoretical improvements by modifying the existing method to reduce its runtime while maintaining its produced sequences. We seek to understand the fundamental mechanisms of the Inexact Penalty Decomposition…
In this BEPE proposal, we intend to study second-order necessary conditions (SONCs) for nonlinear semidefinite and second-order cone programming and the second-order constraint qualifications associated to them. We hope to stablish new sequential optimality conditions and use them to improve some existing results on SONCs for both the mentioned problems, inspired by recent advances in non…
In this BEPE proposal for a long-time stay at Technische Universität Dresden, we are interested in studying strong second-order optimality conditions for nonlinear programming and second-order constraint qualifications associated to them. To the best of our knowledge, no algorithm has been shown to converge to a point at which the strong conditions hold. We are interested in approaching t…
With automatic differentiation, the second-order information of an optimization problem is frequently available for an algorithm seeking its solution. In previous works of the author and his collaborators, we have been interested in identifying first and second order properties of a local minimizer of a general nonlinear optimization problem. Our main interest has been in conditions that …
| 1 / 1 | Ongoing grants |
| 6 / 6 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 12 / 9 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 3 / 3 | Completed scholarships abroad |
| 26 / 23 | All research grants and scholarships |
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