On the Maximization of a Concave Quadratic Function with Box Constraints
- 1 February 1994
- journal article
- research article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Optimization
- Vol. 4 (1) , 177-192
- https://doi.org/10.1137/0804010
Abstract
A new method for maximizing a concave quadratic function with bounds on the variables is introduced. The new algorithm combines conjugate gradients with gradient projection techniques, as the algorithm of More and Toraldo [SIAM J. Optimization, 1 (1991), pp, 93-113] and other well-known methods do. A new strategy for the decision of leaving the current face is introduced that makes it possible to obtain finite convergence even for a singular Hessian and in the presence of dual degeneracy. Numerical experiments are presented.Keywords
This publication has 10 references indexed in Scilit:
- On the Solution of Large Quadratic Programming Problems with Bound ConstraintsSIAM Journal on Optimization, 1991
- Implementing proximal point methods for linear programmingJournal of Optimization Theory and Applications, 1990
- A direct active set algorithm for large sparse quadratic programs with simple boundsMathematical Programming, 1989
- Algorithms for bound constrained quadratic programming problemsNumerische Mathematik, 1989
- A sparse sequential quadratic programming algorithmJournal of Optimization Theory and Applications, 1989
- On the numerical solution of bound constrained optimization problemsRairo-Operations Research, 1989
- Projected Newton Methods for Optimization Problems with Simple ConstraintsSIAM Journal on Control and Optimization, 1982
- A generalized conjugate gradient algorithm for solving a class of quadratic programming problemsLinear Algebra and its Applications, 1980
- Mixed finite elements in ?3Numerische Mathematik, 1980
- Methods of conjugate gradients for solving linear systemsJournal of Research of the National Bureau of Standards, 1952