| bibtype |
J -
Journal Article
|
| ARLID |
0586292 |
| utime |
20240529140042.1 |
| mtime |
20240529235959.9 |
| DOI |
10.1137/23M1557088 |
| title
(primary) (eng) |
Occupation Measure Relaxations in Variational Problems: The Role of Convexity |
| specification |
| page_count |
22 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0255073 |
| ISSN |
1052-6234 |
| title
|
SIAM Journal on Optimization |
| volume_id |
34 |
| volume |
2 (2024) |
| page_num |
1708-1731 |
| publisher |
| name |
SIAM Society for Industrial and Applied Mathematics |
|
|
| keyword |
optimization |
| keyword |
calculus of variations |
| keyword |
occupation measures |
| keyword |
polynomial optimization |
| keyword |
semidefinite programming |
| author
(primary) |
| ARLID |
cav_un_auth*0015534 |
| name1 |
Henrion |
| name2 |
D. |
| country |
FR |
|
| author
|
| ARLID |
cav_un_auth*0468055 |
| name1 |
Korda |
| name2 |
M. |
| country |
FR |
| garant |
K |
|
| author
|
| ARLID |
cav_un_auth*0101142 |
| name1 |
Kružík |
| name2 |
Martin |
| institution |
UTIA-B |
| full_dept (cz) |
Matematická teorie rozhodování |
| full_dept |
Department of Decision Making Theory |
| department (cz) |
MTR |
| department |
MTR |
| full_dept |
Department of Decision Making Theory |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0468056 |
| name1 |
Rios-Zertuche |
| name2 |
R. |
| country |
NO |
|
| source |
|
| source |
|
| cas_special |
| project |
| project_id |
8J20FR019 |
| agency |
GA MŠk |
| ARLID |
cav_un_auth*0397550 |
|
| project |
| project_id |
GX19-26143X |
| agency |
GAČR |
| country |
CZ |
| ARLID |
cav_un_auth*0440774 |
|
| abstract
(eng) |
This work addresses the occupation measure relaxation of calculus of variations problems, which is an infinite-dimensional linear programming reformulation amenable to numerical approximation by a hierarchy of semidefinite optimization problems. We address the problem of equivalence of this relaxation to the original problem. Our main result provides sufficient conditions for this equivalence. These conditions, revolving around the convexity of the data, are simple and apply in very general settings that may be of arbitrary dimensions and may include pointwise and integral constraints, thereby considerably strengthening the existing results. Our conditions are also extended to optimal control problems. In addition, we demonstrate how these results can be applied in nonconvex settings, showing that the occupation measure relaxation is at least as strong as the convexification using the convex envelope; in doing so, we prove that a certain weakening of the occupation measure relaxation is equivalent to the convex envelope. This opens the way to application of the occupation measure relaxation in situations where the convex envelope relaxation is known to be equivalent to the original problem, which includes problems in magnetism and elasticity. |
| result_subspec |
WOS |
| RIV |
BA |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10101 |
| reportyear |
2025 |
| inst_support |
RVO:67985556 |
| permalink |
https://hdl.handle.net/11104/0353845 |
| confidential |
S |
| mrcbC91 |
C |
| mrcbT16-e |
MATHEMATICSAPPLIED |
| mrcbT16-j |
2.356 |
| mrcbT16-D |
Q1* |
| arlyear |
2024 |
| mrcbU14 |
SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
WOS |
| mrcbU63 |
cav_un_epca*0255073 SIAM Journal on Optimization Roč. 34 č. 2 2024 1708 1731 1052-6234 1095-7189 SIAM Society for Industrial and Applied Mathematics |
|