Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method

Yuya Yamakawa () and Hiroyuki Sato ()
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Yuya Yamakawa: Kyoto University
Hiroyuki Sato: Kyoto University

Computational Optimization and Applications, 2022, vol. 81, issue 2, No 3, 397-421

Abstract: Abstract Recently, the approximate Karush–Kuhn–Tucker (AKKT) conditions, also called the sequential optimality conditions, have been proposed for nonlinear optimization in Euclidean spaces, and several methods to find points satisfying such conditions have been developed by researchers. These conditions are known as genuine necessary optimality conditions because all local optima satisfy them with no constraint qualification (CQ). In this paper, we extend the AKKT conditions to nonlinear optimization on Riemannian manifolds and propose an augmented Lagrangian (AL) method that globally converges to points satisfying such conditions. In addition, we prove that the AKKT and KKT conditions are indeed equivalent under a certain CQ. Finally, we examine the effectiveness of the proposed AL method via several numerical experiments.

Keywords: Riemannian manifolds; Riemannian optimization; Sequential optimality conditions; Approximate KKT conditions; Augmented Lagrangian method; Global convergence (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-021-00336-w

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