Algorithm 1035: A Gradient-based Implementation of the Polyhedral Active Set Algorithm

The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over a polyhedron. Phase one of the algorithm is a nonmonotone gradient projection algorithm, while phase two is an active set algorithm that explores faces of the constraint polyhedron. A gradient-based...

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Bibliographic Details
Published inACM transactions on mathematical software Vol. 49; no. 2; pp. 1 - 13
Main Authors Hager, William W., Zhang, Hongchao
Format Journal Article
LanguageEnglish
Published New York, NY ACM 17.06.2023
Subjects
Mathematical optimization
Nonconvex optimization
Theory of computation
PPROJ
NAPHEAP
CG_DESCENT
polyhedral-constrained optimization
gradient projection method
Nonlinear optimization
active set method
PASA
conjugate gradient method
projection on polyhedron
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ISSN0098-3500
1557-7295
1557-7295
DOI10.1145/3583559

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Summary:The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over a polyhedron. Phase one of the algorithm is a nonmonotone gradient projection algorithm, while phase two is an active set algorithm that explores faces of the constraint polyhedron. A gradient-based implementation is presented, where a projected version of the conjugate gradient algorithm is employed in phase two. Asymptotically, only phase two is performed. Comparisons are given with IPOPT using polyhedral-constrained problems from CUTEst and the Maros/Meszaros quadratic programming test set.
ISSN:0098-3500
1557-7295
1557-7295
DOI:10.1145/3583559