A Non-monotone Adaptive Scaled Gradient Projection Method for Orthogonality Constrained Problems

Optimization problems with orthogonality constraints are classical nonconvex nonlinear problems and have been widely applied in science and engineering. In order to solve this problem, we come up with an adaptive scaled gradient projection method. The method combines a scaling matrix that depends on...

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Bibliographic Details
Published in:International journal of applied and computational mathematics Vol. 10; no. 2; p. 89
Main Authors: Ji, Quanming, Zhou, Qinghua
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.04.2024
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Computational Science and Engineering
Convergence
Eigenvalues
Lagrange multiplier
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Optimization
Original Paper
Orthogonality
Theoretical
BB step size
Nonmonotone technique
Adaptive scaled gradient projection method
Stiefel manifold
Orthogonality constraint
ISSN:2349-5103, 2199-5796
Online Access:Get full text
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Summary:Optimization problems with orthogonality constraints are classical nonconvex nonlinear problems and have been widely applied in science and engineering. In order to solve this problem, we come up with an adaptive scaled gradient projection method. The method combines a scaling matrix that depends on the step size with some parameters that control the search direction. In addition, we consider the BB step size and combine a nonmonotone line search technique to accelerate the convergence speed of the proposed algorithm. Under the premise of non-monotonic, we prove the convergence of the algorithm. Also, the computation results proved the efficiency of the proposed algorithm.
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ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-024-01689-6