Sparse convex quadratic programming methods and their applications in projections onto poliedra

• Grant number: 11/04289-0
• Support type: Scholarships in Brazil - Master
• Effective date (Start): August 01, 2011
• Effective date (End): March 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marina Andretta
• Grantee: Jeinny Maria Peralta Polo
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The linearly constrained minimization problem is important, not only for the problem itself, that appears in several areas, but because it is used as a subproblem of more general problems, such as the nonlinear programming problems. In [M. Andretta, E. G. Birgin e J. M. Martínez. Partial spectral projected gradient method with active-set strategy for linearly constrained optimization. Numerical Algorithms 53, pp. 23-52, 2010] was presented an efficient method for solving small and medium scaled linearly constrained minimization problems called GENLIN. To implement a similar method to solve large scale problems, it is necessary to have an efficient method to solve sparse projection problems onto linear constraints. The problem of projecting a point onto a set of linear constraints can be written as a convex quadratic programming problem. the goal of this work is to study and implement sparse methods to solve convex quadratic programming problems, in particular the classical Moré-Toraldo method, compare the performance of the methods when solving the projection onto linear constraints problem and adapt GENLIN to use sparse projections (when it is convenient). (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

POLO, Jeinny Maria Peralta. Métodos de programação quadrática convexa esparsa e suas aplicações em projeções em poliedros. 2013. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação São Carlos.