An active set algorithm for nonlinear optimization with polyhedral constraints

A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provi...

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Veröffentlicht in:Science China. Mathematics Jg. 59; H. 8; S. 1525 - 1542
Hauptverfasser: Hager, William W., Zhang, Hongchao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Beijing Science China Press 01.08.2016
Schlagworte:
Algorithms
Applications of Mathematics
Asymptotic properties
Convergence
Feasibility
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Optimization
Projection
gradient projection algorithm
active set algorithm
polyhedral constrained optimization
local and global convergence
90C06
PASA
90C26
65Y20
ISSN:1674-7283, 1869-1862
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Zusammenfassung:A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-016-0300-6