Deflation for semismooth equations
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination of a semismooth Newton method with a def...
| Váldodahkkit: | , , |
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| Materiálatiipa: | Journal article |
| Giella: | English |
| Almmustuhtton: |
Taylor and Francis
2019
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| _version_ | 1826299487607324672 |
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| author | Farrell, P Croci, M Surowiec, T |
| author_facet | Farrell, P Croci, M Surowiec, T |
| author_sort | Farrell, P |
| collection | OXFORD |
| description | Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination of a semismooth Newton method with a deflation operator that eliminates known solutions from consideration. Given one root of a semismooth resid- ual, deflation constructs a new problem for which a semismooth Newton method will not converge to the known root, even from the same initial guess. This enables the discovery of other roots. We prove the effectiveness of the deflation technique under the same assumptions that guarantee locally superlinear convergence of a semismooth Newton method. We demonstrate its utility on various finite- and infinite-dimensional examples drawn from constrained optimization, game theory, economics and solid mechanics. |
| first_indexed | 2024-03-07T05:02:40Z |
| format | Journal article |
| id | oxford-uuid:d8d7a413-02db-499e-b0b0-836476e61f95 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:02:40Z |
| publishDate | 2019 |
| publisher | Taylor and Francis |
| record_format | dspace |
| spelling | oxford-uuid:d8d7a413-02db-499e-b0b0-836476e61f952022-03-27T08:51:47ZDeflation for semismooth equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d8d7a413-02db-499e-b0b0-836476e61f95EnglishSymplectic Elements at OxfordTaylor and Francis2019Farrell, PCroci, MSurowiec, TVariational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea is the combination of a semismooth Newton method with a deflation operator that eliminates known solutions from consideration. Given one root of a semismooth resid- ual, deflation constructs a new problem for which a semismooth Newton method will not converge to the known root, even from the same initial guess. This enables the discovery of other roots. We prove the effectiveness of the deflation technique under the same assumptions that guarantee locally superlinear convergence of a semismooth Newton method. We demonstrate its utility on various finite- and infinite-dimensional examples drawn from constrained optimization, game theory, economics and solid mechanics. |
| spellingShingle | Farrell, P Croci, M Surowiec, T Deflation for semismooth equations |
| title | Deflation for semismooth equations |
| title_full | Deflation for semismooth equations |
| title_fullStr | Deflation for semismooth equations |
| title_full_unstemmed | Deflation for semismooth equations |
| title_short | Deflation for semismooth equations |
| title_sort | deflation for semismooth equations |
| work_keys_str_mv | AT farrellp deflationforsemismoothequations AT crocim deflationforsemismoothequations AT surowiect deflationforsemismoothequations |