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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Primal-Dual Relationship Between Levenberg-Marquardt and Central Trajectories for Linearly Constrained Convex Optimization

Texto completo
Autor(es):
Behling, Roger [1] ; Gonzaga, Clovis [2] ; Haeser, Gabriel [3]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Catolica SC, Jaragua Do Sul, SC - Brazil
[2] Univ Fed Santa Catarina, Florianopolis, SC - Brazil
[3] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 162, n. 3, p. 705-717, SEP 2014.
Citações Web of Science: 2
Resumo

We consider the minimization of a convex function on a bounded polyhedron (polytope) represented by linear equality constraints and non-negative variables. We define the Levenberg-Marquardt and central trajectories starting at the analytic center using the same parameter, and show that they satisfy a primal-dual relationship, being close to each other for large values of the parameter. Based on this, we develop an algorithm that starts computing primal-dual feasible points on the Levenberg-Marquardt trajectory and eventually moves to the central path. Our main theorem is particularly relevant in quadratic programming, where points on the primal-dual Levenberg-Marquardt trajectory can be calculated by means of a system of linear equations. We present some computational tests related to box constrained trust region subproblems. (AU)

Processo FAPESP: 10/19720-5 - Condições de otimalidade e restauração inexata
Beneficiário:Gabriel Haeser
Linha de fomento: Auxílio à Pesquisa - Apoio a Jovens Pesquisadores