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Practical algorithms for continuous optimization

Grant number: 20/07421-5
Support type:Regular Research Grants
Duration: May 01, 2021 - April 30, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Cooperation agreement: Universidad de la Frontera
Principal researcher:Gabriel Haeser
Grantee:Gabriel Haeser
Principal researcher abroad: Walter Gomez
Institution abroad: Universidad de La Frontera (UFRO), Chile
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Assoc. researchers: Daiana Oliveira dos Santos ; Roberto Andreani

Abstract

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 applications. Our group is interested in developing new optimality conditions without the need of regularity assumptions in such a way as to provide stronger global convergence results for practical algorithms. We are also interested in the applications of such problems for developing tighter convex relaxations for structured non-convex problems such as quadratically constrained quadratic problems. (AU)