Discrete Nonlinear Optimization by State-Space Decompositions
This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently repre...
Saved in:
Published in | Management science Vol. 64; no. 10; pp. 4700 - 4720 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Linthicum
INFORMS
01.10.2018
Institute for Operations Research and the Management Sciences |
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications.
Data and the online appendix are available at
https://doi.org/10.1287/mnsc.2017.2849
.
This paper was accepted by Yinyu Ye, optimization. |
---|---|
AbstractList | This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2849 . This paper was accepted by Yinyu Ye, optimization. This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. History: Accepted by Yinyu Ye, optimization. Funding: The research of A. A. Cire was supported by the Natural Sciences and Engineering Research Council of Canada [Discovery Grant RGPIN-2015-04152]. Supplemental Material: Data and the online appendix are available at Keywords: nonlinear * algorithms * programming * integer * network-graphs * dynamic programming * optimal control * finite state This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on the partition of the objective function into separate low-dimensional dynamic programming (DP) models, each of which can be equivalently represented as a shortest-path problem in an underlying state-transition graph. We show that the associated transition graphs can be related by a mixed-integer linear program (MILP) so as to produce exact solutions to the original nonlinear problem. To address DPs with large state spaces, we present a general relaxation mechanism that dynamically aggregates states during the construction of the transition graphs. The resulting MILP provides both lower and upper bounds to the nonlinear function, and it may be embedded in branch-and-bound procedures to find provably optimal solutions. We describe how to specialize our technique for structured objectives (e.g., submodular functions) and consider three problems arising in revenue management, portfolio optimization, and healthcare. Numerical studies indicate that the proposed technique often outperforms state-of-the-art approaches by orders of magnitude in these applications. Data and the online appendix are available at https://doi.org/10.1287/mnsc.2017.2849 . This paper was accepted by Yinyu Ye, optimization. |
Audience | Trade Academic |
Author | Cire, Andre A. Bergman, David |
Author_xml | – sequence: 1 givenname: David surname: Bergman fullname: Bergman, David – sequence: 2 givenname: Andre A. surname: Cire fullname: Cire, Andre A. |
BookMark | eNqFkt1rHCEUxaUk0E3a174VBgp96mz9WEd96ENI-gUheUj6LOrc2brs6FRdSPrX12FD04WFIijo79zruZwzdBJiAITeELwkVIqPY8huSTERSypX6gVaEE67lnNMTtACY8pborB6ic5y3mCMhRTdAn268tklKNDcxLD1AUxqbqfiR__bFB9DYx-bu2IKtHeTcdBcgYvjFLOfH_MrdDqYbYbXT-c5-vHl8_3lt_b69uv3y4vr1vGOl9Yaafuhl7YbesVcZ4nsjOGdHZzqewwdt6w3HIRS_YowQS2AwBQqqwQwx87Ru33dKcVfO8hFb-IuhdpSU8IIUdULeabWZgvahyGWZNxYDeoLzpVkGCteqfYItYYAyWzrRAdfrw_45RG-rh5G744K3h8IKlPgoazNLmd9CH74B7S7XMef65b9-mfJe_7YR1yKOScY9JT8aNKjJljPCdBzAvScAD0noAre7gWbXGL6S6-kWElG2fMkZlNpzP-r9weAUbxf |
CitedBy_id | crossref_primary_10_1287_opre_2019_1953 crossref_primary_10_1016_j_ejor_2023_12_021 crossref_primary_10_1007_s12532_020_00191_6 crossref_primary_10_1287_trsc_2022_1194 crossref_primary_10_1007_s10601_019_09306_w crossref_primary_10_1287_opre_2022_2353 crossref_primary_10_1287_ijoc_2019_0163 crossref_primary_10_1287_opre_2020_1979 crossref_primary_10_1016_j_disopt_2020_100610 crossref_primary_10_1007_s10107_021_01699_y crossref_primary_10_1007_s10601_017_9280_3 crossref_primary_10_1287_ijoc_2022_1170 crossref_primary_10_1080_24725854_2020_1828668 crossref_primary_10_1287_ijoc_2022_1194 crossref_primary_10_1287_ijoc_2021_1125 crossref_primary_10_1016_j_ejor_2022_03_033 crossref_primary_10_1007_s10107_020_01607_w crossref_primary_10_1016_j_neucom_2022_11_024 |
Cites_doi | 10.1016/j.artint.2006.11.003 10.1007/s10690-014-9180-0 10.1007/978-3-642-15396-9_23 10.1007/978-1-4614-7052-6 10.1007/978-3-642-21311-3_5 10.1287/opre.2013.1221 10.1016/S0378-4266(02)00271-6 10.1287/opre.1070.0445 10.1016/j.dss.2012.10.046 10.1287/opre.2014.1256 10.1287/opre.2015.1471 10.1007/s10288-010-0122-z 10.1109/TC.1986.1676819 10.1287/ijoc.1110.0456 10.1287/ijoc.1110.0461 10.1287/opre.2013.1186 10.1007/3-540-48057-9_15 10.1002/9781118625651 10.1007/s10107-003-0467-6 10.1287/opre.35.6.832 10.1287/opre.38.1.127 10.1017/CBO9781139177801.004 10.1287/opre.2015.1450 10.1007/s00186-012-0408-3 10.1016/j.dam.2012.03.003 10.1017/CBO9780511804441 10.1080/14697681003756877 10.1287/opre.1080.0567 10.1007/3-7643-7374-1 10.1007/978-3-642-38171-3_7 10.1287/ijoc.2015.0648 10.1016/j.orl.2008.04.006 10.1287/msom.1050.0083 10.1287/mnsc.1050.0418 10.1007/s10479-006-0145-1 10.1007/3-540-45622-8_4 10.1080/10556788.2017.1335312 10.1007/s10107-005-0585-4 10.1016/j.ejor.2015.05.053 10.1007/978-1-4757-3155-2 10.1287/opre.2015.1355 10.1287/ijoc.2013.0561 10.1287/mnsc.2015.2312 10.1002/net.3230110207 10.1287/opre.2015.1424 10.1007/s10107-005-0581-8 10.1016/j.sorms.2010.08.001 10.2307/3215235 10.1007/978-3-540-74970-7_11 |
ContentType | Journal Article |
Copyright | 2017 INFORMS COPYRIGHT 2018 Institute for Operations Research and the Management Sciences Copyright Institute for Operations Research and the Management Sciences Oct 2018 |
Copyright_xml | – notice: 2017 INFORMS – notice: COPYRIGHT 2018 Institute for Operations Research and the Management Sciences – notice: Copyright Institute for Operations Research and the Management Sciences Oct 2018 |
DBID | AAYXX CITATION 8BJ FQK JBE |
DOI | 10.1287/mnsc.2017.2849 |
DatabaseName | CrossRef International Bibliography of the Social Sciences (IBSS) International Bibliography of the Social Sciences International Bibliography of the Social Sciences |
DatabaseTitle | CrossRef International Bibliography of the Social Sciences (IBSS) |
DatabaseTitleList | CrossRef |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Business |
EISSN | 1526-5501 |
EndPage | 4720 |
ExternalDocumentID | A559830095 10_1287_mnsc_2017_2849 48748323 mnsc.2017.2849 |
Genre | Research Article |
GeographicLocations | United States |
GeographicLocations_xml | – name: United States |
GroupedDBID | 08R 0R1 1AW 1OL 29M 2AX 3EH 3R3 3V. 4 4.4 41 5GY 6XO 7WY 7X5 85S 8AO 8FI 8FJ 8FL 8VB AABCJ AAIKC AAPBV AAYJJ ABBHK ABEFU ABIVO ABNOP ABPPZ ABSIS ABTRL ABUFD ABUWG ABZEH ACDCL ACHQT ACNCT ACTDY ACVYA ACYGS ADBBV ADDCT ADGDI ADNFJ AEILP AENEX AETEA AEUPB AFDAS AFFDN AFFNX AFKRA AJPNJ AKVCP ALMA_UNASSIGNED_HOLDINGS AQNXB AQSKT AQUVI AZQEC B-7 BBAFP BENPR BEZIV BPHCQ BVXVI CBXGM CCKSF CS3 CWXUR CYVLN DU5 DWQXO EBA EBE EBO EBR EBS EBU ECR EHE EJD EMK EPL F20 F5P FH7 FRNLG FYUFA G8K GENNL GNUQQ GROUPED_ABI_INFORM_ARCHIVE GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GUPYA HGD HVGLF H~9 IAO IEA IGG IOF IPO ISM ITC JAV JBC JPL JSODD JST K6 K60 L8O LI M0C M0T M2M MV1 N95 NEJ NIEAY P-O P2P PQEST PQQKQ PQUKI PRINS PROAC QWB REX RNS RPU SA0 SJN TH9 TN5 U5U UKR VOH VQA WH7 X XFK XHC XI7 XXP XZL Y99 YCJ YNT YZZ ZCG ZL0 -~X 18M AABXT AAMNW AAWTO ABDNZ ABKVW ABXSQ ABYYQ ACGFO ADEPB ADNWM AEGXH AEMOZ AFAIT AFTQD AGHSJ AHAJD AIAGR BAAKF ICW IPC IPY ISL JPPEU K1G K6~ OFU XSW .-4 41~ AAYOK AAYXX ABLWH ADACV ADULT ALIPV CCPQU CITATION IPSME JAAYA JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF LPU PQBIZ PQBZA PSYQQ UKHRP YYP ADMHG 8BJ FQK JBE |
ID | FETCH-LOGICAL-c565t-ba8bdfd8b6fd93c6b186aa56bfc9dd0e65b3da5e799d41372bee702e93c97e3c3 |
ISSN | 0025-1909 |
IngestDate | Fri Sep 13 04:57:27 EDT 2024 Wed May 29 17:40:48 EDT 2024 Wed Oct 02 03:24:46 EDT 2024 Tue May 28 06:10:47 EDT 2024 Sat Sep 28 20:54:03 EDT 2024 Tue May 28 02:01:09 EDT 2024 Thu Sep 12 18:12:42 EDT 2024 Fri Feb 02 07:06:04 EST 2024 Wed Jan 06 02:48:08 EST 2021 |
IsPeerReviewed | true |
IsScholarly | true |
Issue | 10 |
Language | English |
LinkModel | OpenURL |
MergedId | FETCHMERGED-LOGICAL-c565t-ba8bdfd8b6fd93c6b186aa56bfc9dd0e65b3da5e799d41372bee702e93c97e3c3 |
ORCID | 0000-0002-5566-5224 0000-0001-5993-4295 |
PQID | 2131198761 |
PQPubID | 40737 |
PageCount | 21 |
ParticipantIDs | gale_infotracgeneralonefile_A559830095 crossref_primary_10_1287_mnsc_2017_2849 jstor_primary_48748323 informs_primary_10_1287_mnsc_2017_2849 proquest_journals_2131198761 gale_infotracacademiconefile_A559830095 gale_incontextgauss__A559830095 gale_businessinsightsgauss_A559830095 gale_infotracmisc_A559830095 |
ProviderPackageCode | Y99 RPU NIEAY |
PublicationCentury | 2000 |
PublicationDate | 2018-10-01 |
PublicationDateYYYYMMDD | 2018-10-01 |
PublicationDate_xml | – month: 10 year: 2018 text: 2018-10-01 day: 01 |
PublicationDecade | 2010 |
PublicationPlace | Linthicum |
PublicationPlace_xml | – name: Linthicum |
PublicationTitle | Management science |
PublicationYear | 2018 |
Publisher | INFORMS Institute for Operations Research and the Management Sciences |
Publisher_xml | – name: INFORMS – name: Institute for Operations Research and the Management Sciences |
References | B20 B64 B21 B65 B22 B23 B24 B25 B26 B27 B28 B29 B30 B31 B32 B33 B34 B35 B36 B37 B38 B39 B1 B2 B3 B4 B5 B6 B7 B8 B9 B40 B41 B42 B43 B44 B45 B46 B47 B48 B49 B50 B51 B52 B53 B10 B54 B11 B55 B12 B56 B13 B57 B14 B58 B15 B59 B16 B17 B18 B19 B60 B61 B62 B63 Cook WJ (B26) 1998 Sahinidis NV (B56) 2016 Nowak I (B51) 2005; 152 Bertsekas DP (B14) 1999 Derman C (B29) 1970 Birge JR (B17) 1997 Tawarmalani M (B60) 2002; 65 Ahuja RK (B3) 1993 Beardsley XW (B10) 2012; 1 Ebendt R (B31) 2005 Bertsekas DP (B15) 2012 |
References_xml | – ident: B12 – ident: B35 – ident: B60 – ident: B3 – ident: B41 – ident: B45 – ident: B7 – ident: B29 – ident: B64 – ident: B25 – ident: B50 – ident: B21 – ident: B16 – ident: B31 – ident: B58 – ident: B39 – ident: B54 – ident: B61 – ident: B59 – ident: B13 – ident: B2 – ident: B40 – ident: B28 – ident: B44 – ident: B49 – ident: B65 – ident: B6 – ident: B24 – ident: B48 – ident: B17 – ident: B30 – ident: B34 – ident: B51 – ident: B38 – ident: B55 – ident: B9 – ident: B14 – ident: B10 – ident: B43 – ident: B20 – ident: B1 – ident: B27 – ident: B62 – ident: B5 – ident: B47 – ident: B23 – ident: B18 – ident: B33 – ident: B52 – ident: B37 – ident: B56 – ident: B8 – ident: B36 – ident: B11 – ident: B42 – ident: B26 – ident: B4 – ident: B46 – ident: B63 – ident: B22 – ident: B32 – ident: B15 – ident: B57 – ident: B19 – ident: B53 – ident: B28 doi: 10.1016/j.artint.2006.11.003 – volume-title: Dynamic Programming and Optimal Control year: 2012 ident: B15 contributor: fullname: Bertsekas DP – ident: B58 doi: 10.1007/s10690-014-9180-0 – volume-title: Combinatorial Optimization year: 1998 ident: B26 contributor: fullname: Cook WJ – ident: B37 doi: 10.1007/978-3-642-15396-9_23 – ident: B57 doi: 10.1007/978-1-4614-7052-6 – volume-title: Network Flows: Theory, Algorithms, and Applications year: 1993 ident: B3 contributor: fullname: Ahuja RK – ident: B11 doi: 10.1007/978-3-642-21311-3_5 – ident: B23 doi: 10.1287/opre.2013.1221 – ident: B55 doi: 10.1016/S0378-4266(02)00271-6 – ident: B2 doi: 10.1287/opre.1070.0445 – ident: B7 doi: 10.1016/j.dss.2012.10.046 – ident: B27 doi: 10.1287/opre.2014.1256 – ident: B40 doi: 10.1287/opre.2015.1471 – ident: B25 doi: 10.1007/s10288-010-0122-z – volume-title: Advanced BDD Optimization year: 2005 ident: B31 contributor: fullname: Ebendt R – ident: B19 doi: 10.1109/TC.1986.1676819 – ident: B8 doi: 10.1287/ijoc.1110.0456 – volume-title: Nonlinear Programming year: 1999 ident: B14 contributor: fullname: Bertsekas DP – volume: 65 volume-title: Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming—Theory, Algorithms, Software, and Applications year: 2002 ident: B60 contributor: fullname: Tawarmalani M – ident: B6 doi: 10.1287/ijoc.1110.0461 – ident: B52 doi: 10.1287/opre.2013.1186 – ident: B47 doi: 10.1007/3-540-48057-9_15 – volume: 1 start-page: 13 issue: 1 year: 2012 ident: B10 publication-title: Comm. Math. Finance contributor: fullname: Beardsley XW – ident: B34 doi: 10.1002/9781118625651 – ident: B61 doi: 10.1007/s10107-003-0467-6 – ident: B32 doi: 10.1287/opre.35.6.832 – ident: B45 doi: 10.1287/opre.38.1.127 – ident: B41 doi: 10.1017/CBO9781139177801.004 – ident: B33 doi: 10.1287/opre.2015.1450 – ident: B9 doi: 10.1007/s00186-012-0408-3 – ident: B46 doi: 10.1016/j.dam.2012.03.003 – ident: B18 doi: 10.1017/CBO9780511804441 – ident: B36 doi: 10.1080/14697681003756877 – ident: B49 doi: 10.1287/opre.1080.0567 – volume: 152 volume-title: Relaxation and Decomposition Methods for Mixed Integer Nonlinear Programming year: 2005 ident: B51 doi: 10.1007/3-7643-7374-1 contributor: fullname: Nowak I – ident: B38 doi: 10.1007/978-3-642-38171-3_7 – volume-title: Finite State Markovian Decision Processes year: 1970 ident: B29 contributor: fullname: Derman C – ident: B13 doi: 10.1287/ijoc.2015.0648 – ident: B5 doi: 10.1016/j.orl.2008.04.006 – volume-title: Introduction to Stochastic Programming year: 1997 ident: B17 contributor: fullname: Birge JR – ident: B59 doi: 10.1287/msom.1050.0083 – ident: B16 doi: 10.1287/mnsc.1050.0418 – ident: B44 doi: 10.1007/s10479-006-0145-1 – ident: B48 doi: 10.1007/3-540-45622-8_4 – ident: B63 doi: 10.1080/10556788.2017.1335312 – ident: B50 doi: 10.1007/s10107-005-0585-4 – ident: B64 doi: 10.1016/j.ejor.2015.05.053 – ident: B53 doi: 10.1007/978-1-4757-3155-2 – ident: B43 doi: 10.1287/opre.2015.1355 – ident: B12 doi: 10.1287/ijoc.2013.0561 – ident: B21 doi: 10.1287/mnsc.2015.2312 – volume-title: BARON User Manual 16.8.24: Global Optimization of Mixed-Integer Nonlinear Programs year: 2016 ident: B56 contributor: fullname: Sahinidis NV – ident: B22 doi: 10.1002/net.3230110207 – ident: B30 doi: 10.1287/opre.2015.1424 – ident: B62 doi: 10.1007/s10107-005-0581-8 – ident: B42 doi: 10.1016/j.sorms.2010.08.001 – ident: B20 doi: 10.2307/3215235 – ident: B4 doi: 10.1007/978-3-540-74970-7_11 |
SSID | ssj0007876 |
Score | 2.4435217 |
Snippet | This paper investigates a decomposition approach for binary optimization problems with nonlinear objectives and linear constraints. Our methodology relies on... |
SourceID | proquest gale crossref jstor informs |
SourceType | Aggregation Database Publisher |
StartPage | 4700 |
SubjectTerms | algorithms Analysis Artificial intelligence Dynamic programming finite state Health services administration Heuristic integer Linear programming Mathematical optimization network-graphs nonlinear optimal control Optimization Portfolio management programming |
Title | Discrete Nonlinear Optimization by State-Space Decompositions |
URI | https://www.jstor.org/stable/48748323 https://www.proquest.com/docview/2131198761/abstract/ |
Volume | 64 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwELagFagXxKtiS4EcgB5WWZL4kfWhh6W0qpC6INpKvUV27Kx6aFptsgf49Z1JnKyjFvG4WKto4k3mc76ZsWbGhLyXiYql4TbUWoqQGW5ClcsCyFAwZYVRymDt8MlcHJ-zrxf8Yn3qWlNdUutJ_uveupL_QRWuAa5YJfsPyPaTwgX4DfjCCAjD-FcYf7mEjx683vG8bXihluNvQAFXrrYSXcvGmQxPITLGBCFMIO-ytHy3dJ0EM3YmsQ_T7XLhNkm99PfV_oHb024SIsezib97EE_7PDQXUc4h1jw59Rky4SE4CS2NWUeKiQghkol91mx7j3erI_I4kKVR5NlTljbVbne5OsHdjqOrssJOknE6AUMp11apzxWEiIoB7dCHZDNJJYcAe_Pz4fz7j97eAuWI7mBefHLXmhOm_zScfOB6OAP8qO1PW3XpqHdMcuNnnD0lT1yAEMxatJ-RB7Z8Th539QkvSA960IMe-KAH-mfggR4MQX9Jzo8Ozw6OQ3cGRpiDq12HWk21KcxUi8JImgsdT4VSXOgil8ZEVnBNjeI2ldKAP5Im2to0SizIytTSnG6TjfK6tK9IAJGh4lSnmjLDrNUKuJsaig2DDNzERmSvU09207Y6yTBEBEVmqMgMFZmhIkfkA2ovc-ekwlDhTlK1UKuqymbY85-i7z4i7xo57DNSYiJTKzCQ2HMSxXW9VLlyRSHwxNiXbCD5cSC5aLuy3ye4OxAEusyH8zjI__iS282K6MW6hQh_0C2RzJFBlSXYtkrCSox3fnffa7K1_gJ3yUa9XNk34NHW-q1b0rcGuJ-B |
link.rule.ids | 315,786,790,27957,27958,33779 |
linkProvider | ProQuest |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Discrete+Nonlinear+Optimization+by+State-Space+Decompositions&rft.jtitle=Management+science&rft.au=Bergman%2C+David&rft.au=Cire%2C+Andre+A.&rft.date=2018-10-01&rft.pub=INFORMS&rft.issn=0025-1909&rft.eissn=1526-5501&rft.volume=64&rft.issue=10&rft.spage=4700&rft.epage=4720&rft_id=info:doi/10.1287%2Fmnsc.2017.2849&rft.externalDocID=48748323 |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-1909&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-1909&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-1909&client=summon |