Implicit steepest descent algorithm for optimization with orthogonality constraints

Optimization problems with orthogonality constraints appear widely in applications from science and engineering. We address these types of problems from a numerical approach. Our new framework combines the steepest gradient descent, using implicit information, with a projection operator in order to...

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Vydáno v:Optimization letters Ročník 16; číslo 6; s. 1773 - 1797
Hlavní autor: Oviedo, Harry
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Témata:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Eigenvalue problem
Orthogonality constrained optimization
Total energy minimization
Gradient type methods
Riemannian optimization
ISSN:1862-4472, 1862-4480
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Popis
Shrnutí:Optimization problems with orthogonality constraints appear widely in applications from science and engineering. We address these types of problems from a numerical approach. Our new framework combines the steepest gradient descent, using implicit information, with a projection operator in order to construct a feasible sequence of points. In addition, we adopt an adaptive Barzilai–Borwein steplength mixed with a globalization technique in order to speed-up the convergence of our procedure. The global convergence, and some theoretical related to our algorithm are proved. The effectiveness of our proposed algorithm is demonstrated on a variety of problems including Rayleigh quotient maximization, heterogeneous quadratics minimization, weighted orthogonal procrustes problems and total energy minimization. Numerical results show that the new procedure can outperform some state of the art solvers on some practically problems.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01801-5