|Support type:||Scholarships in Brazil - Master|
|Effective date (Start):||June 01, 2012|
|Effective date (End):||April 30, 2014|
|Field of knowledge:||Physical Sciences and Mathematics - Mathematics - Applied Mathematics|
|Principal Investigator:||Ernesto Julián Goldberg Birgin|
|Grantee:||John Lenon Cardoso Gardenghi|
|Home Institution:||Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil|
In the present project the development of an open software to minimize a function subject to equality and inequality linear constraints is aimed. There will be a large number of variables and constraints and, in general, the matrix A that defines the constraints will be a sparse matrix. An interior point approach will be used and, to obtain global convergence, large-scale trust-region problems will be solved. The objective function will be continuous, but the package will also work with LOVO (Low-Order Value Optimization) functions, with relaxed differentiability. The project points to the elaboration of a software that represents the "state-of-art" in this field. John L. C. Gardenghi was medalist in the III Olimpíada Brasileira de Matemática das Escolas Públicas (OBMEP 2007). Between 2008 and 2009 he participated in a junior undergraduate research, supported by CNPq. From 2009 to 2011, he was involved in a undergraduated research also supported by CNPq, under supervision of Prof. Sandra Augusta Santos, from IMECC-UNICAMP. In January and February of this year, the student attended, in the context of the summer school in IME-USP, the course MAT4302 - Tópicos de Álgebra Linear, when he got a A grade. The development of this project will count on the participation of collaborators from other institutions. In this context, Prof. Jose Mario Martinez and Prof. Sandra Augusta Santos, from IMECC-UNICAMP, will be special collaborators. It is planned an intense interaction with these specialists.