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Active set expansion strategies in MPRGP algorithm
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DOI：10.1016/j.advengsoft.2020.102895.png)
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Abstract
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The paper investigates strategies for expansion of active set that can be employed by the MPRGP algorithm. The standard MPRGP expansion uses a projected line search in the free gradient direction with a fixed step length. Such a scheme is often too slow to identify the active set, requiring a large number of expansions. We propose to use adaptive step lengths based on the current gradient, which guarantees the decrease of the unconstrained cost function with different gradient-based search directions. Moreover, we also propose expanding the active set by projecting the optimal step for the unconstrained minimization. Numerical experiments demonstrate the benefits (up to 78% decrease in the number of Hessian multiplications) of our expansion step modifications on two benchmarks - contact problem of linear elasticity solved by TFETI and machine learning problems of SVM type, both implemented in PERMON toolbox.
Keywords:
MPRGP
Active set
Expansion step
Quadratic programming
PERMON
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