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: constraint qualifications, nonlinear programming, optimality conditions, global convergence and stopping criteria. (Source: Lattes Curriculum)
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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,…
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…
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)
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…
In the context of necessary optimality condition for nonlinear optimization and semidefinite optimization, the complementarity measure may be defined in several equivalent ways. However, in its sequential counterparts, where no constraint qualification is assumed, the way the complementarity is defined impacts the strength of the optimality condition. Our goul in this project is to study …
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 …
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…
In this project we will approach algorithms to the general smooth nonlinear optimization problem. Given that an algorithm has stopped due to satisfying its optimality criterium with some precision, we intend to estimate the distance between the output solution and an actual stationary point of the problem, imposing some weak hypothesis over it. This leads to an accurate quality measure of…
(Only some records are available in English at this moment)
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 research grants |
| 5 / 5 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 10 / 7 | Completed scholarships in Brazil |
| 3 / 3 | Completed scholarships abroad |
| 21 / 18 | All research grants and scholarships |
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