Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem
In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computat...
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| Vydáno v: | Acta Mathematicae Applicatae Sinica Ročník 30; číslo 3; s. 707 - 720 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2014
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| Témata: | |
| ISSN: | 0168-9673, 1618-3932 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved. |
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| Bibliografie: | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved. 11-2041/O1 nonlinear programming; large-scale minimization; parallel algorithm; constrained convex opti-mization |
| ISSN: | 0168-9673 1618-3932 |
| DOI: | 10.1007/s10255-013-0300-9 |