Towards an efficient augmented Lagrangian method for convex quadratic programming

Autor(es)

Bueno, Luis Felipe ^[1] ; Haeser, Gabriel ^[2] ; Santos, Luiz-Rafael ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Sao Paulo, SP - Brazil

^[3] Univ Fed Santa Catarina, Dept Math, Blumenau, SC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 76, n. 3, SI, p. 767-800, JUL 2020.
• Citações Web of Science: 3

Resumo

Interior point methods have attracted most of the attention in the recent decades for solving large scale convex quadratic programming problems. In this paper we take a different route as we present an augmented Lagrangian method for convex quadratic programming based on recent developments for nonlinear programming. In our approach, box constraints are penalized while equality constraints are kept within the subproblems. The motivation for this approach is that Newton's method can be efficient for minimizing a piecewise quadratic function. Moreover, since augmented Lagrangian methods do not rely on proximity to the central path, some of the inherent difficulties in interior point methods can be avoided. In addition, a good starting point can be easily exploited, which can be relevant for solving subproblems arising from sequential quadratic programming, in sensitivity analysis and in branch and bound techniques. We prove well-definedness and finite convergence of the method proposed. Numerical experiments on separable strictly convex quadratic problems formulated from theNetlibcollection show that our method can be competitive with interior point methods, in particular when a good initial point is available and a second-order Lagrange multiplier update is used. (AU)

• Processo FAPESP: 18/24293-0 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/02528-8 - Métodos do tipo Newton para otimização linear e não linear
• Beneficiário: Luis Felipe Cesar da Rocha Bueno
• Modalidade de apoio: Auxílio à Pesquisa - Regular