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On solutions of sparsity constrained optimization

On solutions of sparsity constrained optimization
On solutions of sparsity constrained optimization
In this paper, we mainly study the existence of solutions to sparsity constrained optimization (SCO). Based on the expressions of tangent cone and normal cone of sparsity constraint, we present and characterize two first-order necessary optimality conditions for SCO: N-stationarity and T-stationarity. Then we give the second-order necessary and sufficient optimality conditions for SCO. At last, we extend these results to SCO with nonnegative constraint.
2194-668X
421-439
Pan, Lili
432e64ee-1662-440e-88e7-de32dddf453e
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3
Pan, Lili
432e64ee-1662-440e-88e7-de32dddf453e
Xiu, Naihua
8b5770f7-ae35-4dbe-884a-02fb4ea27bee
Zhou, Shenglong
d183edc9-a9f6-4b07-a140-a82213dbd8c3

Pan, Lili, Xiu, Naihua and Zhou, Shenglong (2015) On solutions of sparsity constrained optimization. Journal of the Operations Research Society of China, 3 (4), 421-439. (doi:10.1007/s40305-015-0101-3).

Record type: Article

Abstract

In this paper, we mainly study the existence of solutions to sparsity constrained optimization (SCO). Based on the expressions of tangent cone and normal cone of sparsity constraint, we present and characterize two first-order necessary optimality conditions for SCO: N-stationarity and T-stationarity. Then we give the second-order necessary and sufficient optimality conditions for SCO. At last, we extend these results to SCO with nonnegative constraint.

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More information

Published date: 30 October 2015

Identifiers

Local EPrints ID: 442410
URI: http://eprints.soton.ac.uk/id/eprint/442410
DOI: doi:10.1007/s40305-015-0101-3
ISSN: 2194-668X
PURE UUID: cabd263e-2823-4a68-80bf-c1f7b37d0da2
ORCID for Shenglong Zhou: ORCID iD orcid.org/0000-0003-2843-1614

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Date deposited: 14 Jul 2020 16:39
Last modified: 16 Mar 2024 08:32

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Contributors

Author: Lili Pan
Author: Naihua Xiu
Author: Shenglong Zhou ORCID iD

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