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A block active set algorithm for large-scale quadratic programming with box constraints.

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Title: A block active set algorithm for large-scale quadratic programming with box constraints.
Authors: Fernandes, L.1, Fischer, A.2, Júdice, J.3, Requejo, C.3, Soares, J.3
Source: Annals of Operations Research. 1998, Vol. 81 Issue 1-4, p75-95. 21p. 4 Charts.
Subjects: Computer software, Sparse matrix software, Quadratic programming, Nonlinear programming, Algorithms, Mathematical programming, Mathematical analysis, Operations research
Abstract: An algorithm for computing a stationary point of a quadratic program with box constraints (BQP) is proposed. Each iteration of this procedure comprises a guessing strategy which forecasts the active bounds at a stationary point, the determination of a descent direction by means of solving a reduced strictly convex quadratic program with box constraints and an exact line search. Global convergence is established in the sense that every accumulation point is stationary. Moreover, it is shown that the algorithm terminates after a finite number of iterations, if at least one iterate is sufficiently close to a stationary point which satisfies a certain sufficient optimality condition. The algorithm can be easily implemented for sparse large-scale BQPs. Furthermore, it simplifies for concave BQPs, as it is not required to solve strictly convex quadratic programs in this case. Computational experience with large-scale BQPs is included and shows the appropriateness of this type of methodology. [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: An algorithm for computing a stationary point of a quadratic program with box constraints (BQP) is proposed. Each iteration of this procedure comprises a guessing strategy which forecasts the active bounds at a stationary point, the determination of a descent direction by means of solving a reduced strictly convex quadratic program with box constraints and an exact line search. Global convergence is established in the sense that every accumulation point is stationary. Moreover, it is shown that the algorithm terminates after a finite number of iterations, if at least one iterate is sufficiently close to a stationary point which satisfies a certain sufficient optimality condition. The algorithm can be easily implemented for sparse large-scale BQPs. Furthermore, it simplifies for concave BQPs, as it is not required to solve strictly convex quadratic programs in this case. Computational experience with large-scale BQPs is included and shows the appropriateness of this type of methodology. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: 1998
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