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Title: Projected nonmonotone search methods for optimization with orthogonality constraints

Abstract

In this paper, we propose two feasible methods based on projections using a curvilinear search for solving optimization problems with orthogonality constraints. In one of them we apply a projected Adams–Moulton-like update scheme. All our algorithms compute the SVD decomposition in each iteration to preserve feasibility. Additionally, we present some convergence results. Finally, we perform numerical experiments with simulated problems; and analyze the performance of the proposed methods compared with state-of-the-art algorithms.

Authors:
;  [1]
  1. CIMAT A.C., Mathematics Research Center (Mexico)
Publication Date:
OSTI Identifier:
22769283
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; COMPARATIVE EVALUATIONS; CONVERGENCE; OPTIMIZATION; PERFORMANCE; SIMULATION

Citation Formats

Dalmau Cedeño, Oscar Susano, E-mail: dalmau@cimat.mx, and Oviedo Leon, Harry Fernando, E-mail: harry.oviedo@cimat.mx. Projected nonmonotone search methods for optimization with orthogonality constraints. United States: N. p., 2018. Web. doi:10.1007/S40314-017-0501-6.
Dalmau Cedeño, Oscar Susano, E-mail: dalmau@cimat.mx, & Oviedo Leon, Harry Fernando, E-mail: harry.oviedo@cimat.mx. Projected nonmonotone search methods for optimization with orthogonality constraints. United States. doi:10.1007/S40314-017-0501-6.
Dalmau Cedeño, Oscar Susano, E-mail: dalmau@cimat.mx, and Oviedo Leon, Harry Fernando, E-mail: harry.oviedo@cimat.mx. Sun . "Projected nonmonotone search methods for optimization with orthogonality constraints". United States. doi:10.1007/S40314-017-0501-6.
@article{osti_22769283,
title = {Projected nonmonotone search methods for optimization with orthogonality constraints},
author = {Dalmau Cedeño, Oscar Susano, E-mail: dalmau@cimat.mx and Oviedo Leon, Harry Fernando, E-mail: harry.oviedo@cimat.mx},
abstractNote = {In this paper, we propose two feasible methods based on projections using a curvilinear search for solving optimization problems with orthogonality constraints. In one of them we apply a projected Adams–Moulton-like update scheme. All our algorithms compute the SVD decomposition in each iteration to preserve feasibility. Additionally, we present some convergence results. Finally, we perform numerical experiments with simulated problems; and analyze the performance of the proposed methods compared with state-of-the-art algorithms.},
doi = {10.1007/S40314-017-0501-6},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 3,
volume = 37,
place = {United States},
year = {2018},
month = {7}
}