Signomial and polynomial optimization via relative entropy and partial dualization
We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way w...
Saved in:
| Published in | Mathematical programming computation Vol. 13; no. 2; pp. 257 - 295 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way which enables partial dualization of certain structured constraints. This more general approach retains key properties of ordinary SAGE relaxations (e.g. sparsity preservation), and inspires a projective method of solution recovery which respects partial dualization. We illustrate the utility of our methodology with a range of examples from the global optimization literature, along with a publicly available software package. |
|---|---|
| AbstractList | We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial optimization problems. Our approach leverages the fact that SAGE certificates conveniently and transparently blend with convex duality, in a way which enables partial dualization of certain structured constraints. This more general approach retains key properties of ordinary SAGE relaxations (e.g. sparsity preservation), and inspires a projective method of solution recovery which respects partial dualization. We illustrate the utility of our methodology with a range of examples from the global optimization literature, along with a publicly available software package. |
| Author | Chandrasekaran, Venkat Wierman, Adam Murray, Riley |
| Author_xml | – sequence: 1 givenname: Riley surname: Murray fullname: Murray, Riley email: rmurray@caltech.edu organization: California Institute of Technology – sequence: 2 givenname: Venkat surname: Chandrasekaran fullname: Chandrasekaran, Venkat organization: California Institute of Technology – sequence: 3 givenname: Adam surname: Wierman fullname: Wierman, Adam organization: California Institute of Technology |
| BookMark | eNp9kMtqAyEUhqWk0DTNC3Q10LXtUWfiuCyhNygUelmLo04wTHSqk0D69DWd0O7qwuOB7z_qd44mPniL0CWBawLAbxKhFaMYKGAAIhguT9CU1AuOqaj45PdcijM0T2kNeTHKayam6PXNrXzYONUVypuiD93-2IZ-cBv3pQYXfLFzqoi2y83OFtYPMfT7MaDicKDNVnVH-AKdtqpLdn6sM_Rxf_e-fMTPLw9Py9tnrBkRA84PbdrS8opVwLQWxNamaUnN8wZ1YxgYo20tmlwXmhndKrOgjdCagzZtw2boapzbx_C5tWmQ67CNPl8ps4-qzh8Emik6UjqGlKJtZR_dRsW9JCAP-uSoT2Z98kefLHOIjaGUYb-y8W_0P6lvL4p2wg |
| CitedBy_id | crossref_primary_10_1007_s12532_022_00226_0 crossref_primary_10_1137_21M1422574 crossref_primary_10_1137_22M1484511 crossref_primary_10_1137_20M1313969 crossref_primary_10_1137_21M1462568 crossref_primary_10_1137_22M1504548 crossref_primary_10_1007_s10107_022_01776_w crossref_primary_10_1137_21M1405691 crossref_primary_10_1007_s10013_021_00528_1 crossref_primary_10_1007_s13366_020_00512_9 crossref_primary_10_1137_22M1530410 |
| Cites_doi | 10.1109/CDC.2012.6426491 10.1108/03321640710727809 10.1007/s12532-017-0121-6 10.1137/18M118935X 10.1007/s10898-008-9382-y 10.1007/BF01070233 10.1007/978-0-387-09686-5_7 10.1007/978-94-015-8330-5_4 10.1016/S0096-3003(03)00200-5 10.1007/s13675-015-0050-y 10.3934/dcdsb.2012.17.2153 10.1007/BF01442738 10.1137/140988978 10.1007/BF00934080 10.1007/s11590-019-01422-z 10.1007/s10898-008-9283-0 10.1007/BF00933404 10.6010/geoinformatics1975.1976.2_66 10.1016/j.amc.2005.01.142 10.1007/978-0-387-31256-9 10.1007/978-0-387-75714-8_5 10.1145/1577190.1577212 10.2514/1.C034378 10.1016/j.amc.2006.05.208 10.1080/10556780802699201 10.1145/3313831.3376412 10.1007/BF02592948 10.5281/ZENODO.4017991 10.1016/j.amc.2006.05.137 10.1186/s40687-016-0052-2 10.1007/978-0-387-88757-9_6 10.1090/S0002-9947-00-02595-2 10.1137/S1052623400366802 10.1017/CBO9781107447226 10.1016/j.ejor.2013.10.016 10.1145/317275.317286 10.1155/2014/158375 10.23919/ECC.2013.6669541 |
| ContentType | Journal Article |
| Copyright | Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020 Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020. |
| Copyright_xml | – notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020 – notice: Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2020. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s12532-020-00193-4 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1867-2957 |
| EndPage | 295 |
| ExternalDocumentID | 10_1007_s12532_020_00193_4 |
| GroupedDBID | -5D -5G -BR -EM -~C 06D 0R~ 0VY 1N0 203 29M 2JY 2KG 2VQ 2~H 30V 4.4 406 408 409 40D 40E 6NX 8UJ 96X AAAVM AAFGU AAHNG AAIAL AAJKR AANZL AAPBV AARHV AARTL AATNV AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO AAZMS ABBXA ABDZT ABECU ABFGW ABFTV ABHLI ABHQN ABJNI ABJOX ABKAS ABKCH ABMQK ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACBMV ACBRV ACBYP ACGFS ACHSB ACIGE ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACTTH ACVWB ACWMK ADHHG ADHIR ADINQ ADKNI ADKPE ADMDM ADOXG ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFTE AEGNC AEJHL AEJRE AEKMD AEOHA AEPYU AESKC AESTI AEVLU AEVTX AEXYK AFLOW AFNRJ AFQWF AFWTZ AFZKB AGAYW AGDGC AGGBP AGJBK AGMZJ AGQMX AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO AJZVZ AKQUC ALFXC ALMA_UNASSIGNED_HOLDINGS AMKLP AMXSW AMYLF AMYQR ANMIH AOCGG ASPBG AUKKA AVWKF AXYYD AYJHY AZFZN BA0 BAPOH BGNMA CAG COF CSCUP DDRTE DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FYJPI GGCAI GGRSB GJIRD GQ6 GQ7 GQ8 GXS HF~ HG6 HLICF HMJXF HQYDN HRMNR HZ~ I0C IJ- IKXTQ IWAJR IXC IXD IZIGR I~X J-C J0Z J9A JBSCW JCJTX JZLTJ KOV LLZTM M4Y NPVJJ NQJWS NU0 O9- O93 O9J OAM OK1 P9R PT4 QOS R89 RIG RLLFE ROL RSV S1Z S27 S3B SDH SHX SISQX SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE T13 TSG U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W48 WK8 Z45 Z7Y Z83 Z88 ZMTXR ~A9 AACDK AAJBT AASML AAYXX ABAKF ACAOD ACDTI ACZOJ AEFQL AEMSY AFBBN AGQEE AGRTI AIGIU CITATION H13 SJYHP |
| ID | FETCH-LOGICAL-c319t-193bf4e753503cc91e8dbf187bf108bd30ddce89b0dd6c3dcfad62b9cc70cdfb3 |
| IEDL.DBID | U2A |
| ISSN | 1867-2949 |
| IngestDate | Mon Oct 07 11:39:02 EDT 2024 Thu Sep 12 18:34:16 EDT 2024 Sat Dec 16 12:09:54 EST 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Signomial programming Exponential cone programs Global optimization SAGE certificates SOS certificates |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c319t-193bf4e753503cc91e8dbf187bf108bd30ddce89b0dd6c3dcfad62b9cc70cdfb3 |
| PQID | 2535878302 |
| PQPubID | 2044128 |
| PageCount | 39 |
| ParticipantIDs | proquest_journals_2535878302 crossref_primary_10_1007_s12532_020_00193_4 springer_journals_10_1007_s12532_020_00193_4 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-06-01 |
| PublicationDateYYYYMMDD | 2021-06-01 |
| PublicationDate_xml | – month: 06 year: 2021 text: 2021-06-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationSubtitle | A Publication of the Mathematical Optimization Society |
| PublicationTitle | Mathematical programming computation |
| PublicationTitleAbbrev | Math. Prog. Comp |
| PublicationYear | 2021 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Shao-JianQZhangK-CJiYA new global optimization algorithm for signomial geometric programming via Lagrangian relaxationAppl. Math. Comput.2007184288689422949551116.65071 Verschelde, J.: Algorithm 795: PHCpack—a general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Softw. 25(2), 251–276 (1999). issn: 0098-3500 AgrawalADiamondSBoydSDisciplined geometric programmingOptim. Lett.2019135961976395698410.1007/s11590-019-01422-z Powell, M.J.D.: A direct search optimization method that models the objective and constraint functions by linear interpolation. In: Advances in Optimization and Numerical Analysis, Springer, Dordrecht, pp. 51–67. ISBN: 978-94-015-8330-5 (1994) ChandrasekaranVShahPRelative entropy relaxations for signomial optimizationSIAM J. Optim.201626211471173349955910.1137/140988978 ShenPJiaoHA new rectangle branch-and-pruning approach for generalized geometric programmingAppl. Math. Comput.200618321027103822908571112.65058 Jabr, R.A.: Inductor design using signomial programming. COM-PEL Int. J. Comput. Math. Electr. Electron. Eng. 26(2), 461–475 (2007) Serrano, S.A.: Algorithms for unsymmetric cone optimization and an implementation for problems with the exponential cone. PhD Thesis, Stanford University, Palo Alto, CA (2015) Surjanovic, S., Bingham, D.: Virtual library of simulation experiments: test functions and datasets. Retrieved April 18 from http://www.sfu.ca/~ssurjano (2019) August, E., Craciun, G., Koeppl, H.: Finding invariant sets for biological systems using monomial domination. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), IEEE (2012) Rijckaert, M.J., Martens, X.M.: Comparison of generalized geometric programming algorithms. J. Optim. Theory Appl. 26(2), 205–242 (1978). issn: 1573-2878 Parrilo, P.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD thesis, California Institute of Technology (2000) Wang, Y., Liang, Z.: A deterministic global optimization algorithm for generalized geometric programming. Appl. Math. Comput. 168(1), 722–737 (2005). issn: 0096-3003 PowersVReznickBPolynomials that are positive on an intervalTrans. Am. Math. Soc.20003521046774692170720310.1090/S0002-9947-00-02595-2 IlimanSde WolffTAmoebas, nonnegative polynomials and sums of squares supported on circuitsRes. Math. Sci.201639348119510.1186/s40687-016-0052-2 Burnell, E., Damen, N.B., Hoburg, W.: GPkit: a human-centered approach to convex optimization in engineering design. In: Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems (2020) Vandenberghe, L.: The CVXOPT linear and quadratic cone program solvers (2010). http://www.seas.ucla.edu/~vandenbe/publications/coneprog.pdf Forsgård, J., de Wolff, T.: The algebraic boundary of the sonc cone (2019). arXiv:1905.04776 Pébay, P.P., Rojas, J.M., Thompson, D.C.: Optimization and NP R-completeness of certain fewnomials. In: Proceedings of the 2009 Conference on Symbolic Numeric Computation, ACM Press (2009) Bard, G.V.: Some basic facts about linear algebra over GF(2). In: Algebraic Cryptanalysis, Springer, Berlin, pp. 81–88 (2009) RaySNatarajPSVAn efficient algorithm for range computation of polynomials using the Bernstein formJ. Global Optim.2008453403426255021810.1007/s10898-008-9382-y Yan, J.: Signomial programs with equality constraints: numerical solution and applications. PhD thesis, University of British Columbia (1976) AhmadiAAMajumdarADSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimizationSIAM J. Appl. Algebra Geom.201932193230393932110.1137/18M118935X Domahidi, A., Chu, E., Boyd, S.: ECOS: an SOCP solver for embedded systems. In: European Control Conference (ECC), pp. 3071–3076 (2013) GongxianXGlobal optimization of signomial geometric programming problemsEur. J. Oper. Res.20142333500510313132510.1016/j.ejor.2013.10.016 Laurent, M.: Sums of squares, moment matrices and optimization over polynomials. In: Putinar, M., Sullivant, S. (eds.) Emerging Applications of Algebraic Geometry, pp. 157–270. Springer, New York (2009). isbn: 978-0-387-09686-5 Lasserre, J.B., Toh, K.-C., Yang, S.: A bounded degree SOS hierarchy for polynomial optimization. EURO J. Comput. Optim. 5(1), 87–117 (2017). issn: 2192- 4414 Murty, K.G., Kabadi, S.N.: Some NP-complete problems in quadratic and nonlinear programming. Math. Program. 39(2), 117–129 (1987). issn: 1436-4646 Weisser, T., Lasserre, J.B., Toh, K.-C.: Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity. Math. Program. Comput. 10(1), 1–32 (2018). issn: 1867-2957 Katthän, L., Naumann, H., Theobald, T.: A unified framework of SAGE and SONC polynomials and its duality theory (2019). arXiv:1903.08966 BorweinJLewisAConvex Analysis and Nonlinear Optimization2006New YorkSpringer10.1007/978-0-387-31256-9 ShorNZClass of global minimum bounds of polynomial functionsCybernetics198723673173410.1007/BF01070233 Wang, J.: Nonnegative polynomials and circuit polynomials (2018). arXiv:1804.09455 LasserreJBAn Introduction to Polynomial and Semi-algebraic OptimizationCambridge Texts in Applied Mathematics2015CambridgeCambridge University Press10.1017/CBO9781107447226 Murray, R.: Sageopt 0.5.3 (2020). https://doi.org/10.5281/ZENODO.4017991 Seidler, H., de Wolff, T.: POEM: effective methods in polynomial optimization, version 0.2.1.0(a) (2019). http://www.iaa.tu-bs.de/AppliedAlgebra/POEM/index.html HenrionDLasserreJ-BLöfbergJGloptiPoly 3: moments, optimization and semidefinite programmingOptim. Methods Softw.2009244–5761779255491010.1080/10556780802699201 Chiang, M.: Nonconvex optimization for communication networks. In: Honor of Gilbert Strang, Advances in Applied Mathematics and Global Optimization, Springer US, Boston, pp. 137–196. ISBN: 978-0-387-75714-8 (2009) Seidler, H., de Wolff, T.: An experimental comparison of SONC and SOS certificates for unconstrained optimization (2018). arXiv:1808.08431 ShenPZhangKGlobal optimization of signomial geometric programming using linear relaxationAppl. Math. Comput.200415019911420343701053.90112 ReznickBForms derived from the arithmetic-geometric inequalityMath. Ann.1989283343146498524110.1007/BF01442738 PanteaCKoepplHCraciunGGlobal injectivity and multiple equilibria in uni- and bi-molecular reaction networksDiscrete Contin. Dyn. Syst. Ser. B201217621532170292445510.3934/dcdsb.2012.17.2153 KirschenPGApplication of signomial programming to aircraft designJ. Aircr.201855396598710.2514/1.C034378 LasserreJBGlobal optimization with polynomials and the problem of momentsSIAM J. Optim.2001113796817181404510.1137/S1052623400366802 MOSEK ApS. MOSEK 9.0.70(beta) (2019) Rountree, D.H., Rigler, A.K.: A penalty treatment of equality constraints in generalized geometric programming. J. Optim. Theory Appl. 38(2), 169–178 (1982). issn: 1573-2878 Murray, R., Chandrasekaran, V., Wierman, A.: Newton polytopes and relative entropy optimization (2018). arXiv:1810.01614 Shen, P., Ma, Y., Chen, Y.: A robust algorithm for generalized geometric programming. J. Global Optim. 41(4), 593–612 (2008). issn: 1573-2916 HouXShenPChenYA global optimization algorithm for signomial geometric programming problemAbstract Appl. Anal.20142014112319348910.1155/2014/158375 Papachristodoulou, A., et al.: SOSTOOLS version 3.00 sum of squares optimization toolbox for MATLAB (2013). arXiv:1310.4716 PG Kirschen (193_CR2) 2018; 55 S Iliman (193_CR17) 2016; 3 P Shen (193_CR7) 2006; 183 193_CR29 V Powers (193_CR30) 2000; 352 JB Lasserre (193_CR33) 2015 193_CR27 193_CR25 193_CR26 193_CR23 193_CR24 193_CR21 S Ray (193_CR39) 2008; 45 193_CR3 193_CR4 193_CR6 X Hou (193_CR10) 2014; 2014 193_CR9 C Pantea (193_CR22) 2012; 17 193_CR18 193_CR19 193_CR16 A Agrawal (193_CR36) 2019; 13 AA Ahmadi (193_CR48) 2019; 3 193_CR13 193_CR1 193_CR50 V Chandrasekaran (193_CR15) 2016; 26 D Henrion (193_CR28) 2009; 24 193_CR49 193_CR47 Q Shao-Jian (193_CR8) 2007; 184 193_CR45 193_CR46 193_CR43 193_CR44 193_CR41 193_CR42 193_CR40 P Shen (193_CR5) 2004; 150 J Borwein (193_CR32) 2006 JB Lasserre (193_CR14) 2001; 11 NZ Shor (193_CR12) 1987; 23 193_CR38 B Reznick (193_CR20) 1989; 283 193_CR37 X Gongxian (193_CR11) 2014; 233 193_CR34 193_CR35 193_CR31 |
| References_xml | – ident: 193_CR26 – ident: 193_CR23 doi: 10.1109/CDC.2012.6426491 – ident: 193_CR49 – ident: 193_CR3 doi: 10.1108/03321640710727809 – ident: 193_CR41 doi: 10.1007/s12532-017-0121-6 – volume: 3 start-page: 193 issue: 2 year: 2019 ident: 193_CR48 publication-title: SIAM J. Appl. Algebra Geom. doi: 10.1137/18M118935X contributor: fullname: AA Ahmadi – volume: 45 start-page: 403 issue: 3 year: 2008 ident: 193_CR39 publication-title: J. Global Optim. doi: 10.1007/s10898-008-9382-y contributor: fullname: S Ray – volume: 23 start-page: 731 issue: 6 year: 1987 ident: 193_CR12 publication-title: Cybernetics doi: 10.1007/BF01070233 contributor: fullname: NZ Shor – ident: 193_CR31 doi: 10.1007/978-0-387-09686-5_7 – ident: 193_CR34 doi: 10.1007/978-94-015-8330-5_4 – volume: 150 start-page: 99 issue: 1 year: 2004 ident: 193_CR5 publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(03)00200-5 contributor: fullname: P Shen – ident: 193_CR13 – ident: 193_CR27 – ident: 193_CR40 doi: 10.1007/s13675-015-0050-y – volume: 17 start-page: 2153 issue: 6 year: 2012 ident: 193_CR22 publication-title: Discrete Contin. Dyn. Syst. Ser. B doi: 10.3934/dcdsb.2012.17.2153 contributor: fullname: C Pantea – ident: 193_CR50 – volume: 283 start-page: 431 issue: 3 year: 1989 ident: 193_CR20 publication-title: Math. Ann. doi: 10.1007/BF01442738 contributor: fullname: B Reznick – ident: 193_CR44 – volume: 26 start-page: 1147 issue: 2 year: 2016 ident: 193_CR15 publication-title: SIAM J. Optim. doi: 10.1137/140988978 contributor: fullname: V Chandrasekaran – ident: 193_CR1 doi: 10.1007/BF00934080 – volume: 13 start-page: 961 issue: 5 year: 2019 ident: 193_CR36 publication-title: Optim. Lett. doi: 10.1007/s11590-019-01422-z contributor: fullname: A Agrawal – ident: 193_CR16 – ident: 193_CR9 doi: 10.1007/s10898-008-9283-0 – ident: 193_CR46 doi: 10.1007/BF00933404 – ident: 193_CR35 doi: 10.6010/geoinformatics1975.1976.2_66 – ident: 193_CR6 doi: 10.1016/j.amc.2005.01.142 – volume-title: Convex Analysis and Nonlinear Optimization year: 2006 ident: 193_CR32 doi: 10.1007/978-0-387-31256-9 contributor: fullname: J Borwein – ident: 193_CR47 – ident: 193_CR4 doi: 10.1007/978-0-387-75714-8_5 – ident: 193_CR21 doi: 10.1145/1577190.1577212 – volume: 55 start-page: 965 issue: 3 year: 2018 ident: 193_CR2 publication-title: J. Aircr. doi: 10.2514/1.C034378 contributor: fullname: PG Kirschen – ident: 193_CR24 – volume: 184 start-page: 886 issue: 2 year: 2007 ident: 193_CR8 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.05.208 contributor: fullname: Q Shao-Jian – volume: 24 start-page: 761 issue: 4–5 year: 2009 ident: 193_CR28 publication-title: Optim. Methods Softw. doi: 10.1080/10556780802699201 contributor: fullname: D Henrion – ident: 193_CR45 doi: 10.1145/3313831.3376412 – ident: 193_CR18 doi: 10.1007/BF02592948 – ident: 193_CR42 doi: 10.5281/ZENODO.4017991 – volume: 183 start-page: 1027 issue: 2 year: 2006 ident: 193_CR7 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2006.05.137 contributor: fullname: P Shen – volume: 3 start-page: 9 year: 2016 ident: 193_CR17 publication-title: Res. Math. Sci. doi: 10.1186/s40687-016-0052-2 contributor: fullname: S Iliman – ident: 193_CR37 doi: 10.1007/978-0-387-88757-9_6 – ident: 193_CR19 – volume: 352 start-page: 4677 issue: 10 year: 2000 ident: 193_CR30 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-00-02595-2 contributor: fullname: V Powers – volume: 11 start-page: 796 issue: 3 year: 2001 ident: 193_CR14 publication-title: SIAM J. Optim. doi: 10.1137/S1052623400366802 contributor: fullname: JB Lasserre – volume-title: An Introduction to Polynomial and Semi-algebraic OptimizationCambridge Texts in Applied Mathematics year: 2015 ident: 193_CR33 doi: 10.1017/CBO9781107447226 contributor: fullname: JB Lasserre – ident: 193_CR25 – volume: 233 start-page: 500 issue: 3 year: 2014 ident: 193_CR11 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2013.10.016 contributor: fullname: X Gongxian – ident: 193_CR29 – ident: 193_CR38 doi: 10.1145/317275.317286 – volume: 2014 start-page: 1 year: 2014 ident: 193_CR10 publication-title: Abstract Appl. Anal. doi: 10.1155/2014/158375 contributor: fullname: X Hou – ident: 193_CR43 doi: 10.23919/ECC.2013.6669541 |
| SSID | ssj0000327839 |
| Score | 2.4097369 |
| Snippet | We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for relative entropy relaxations of constrained signomial and polynomial... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Publisher |
| StartPage | 257 |
| SubjectTerms | Constraints Entropy Full Length Paper Global optimization Mathematics Mathematics and Statistics Mathematics of Computing Operations Research/Decision Theory Optimization Polynomials Theory of Computation |
| Title | Signomial and polynomial optimization via relative entropy and partial dualization |
| URI | https://link.springer.com/article/10.1007/s12532-020-00193-4 https://www.proquest.com/docview/2535878302/abstract/ |
| Volume | 13 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LSwMxEB60vehBfGK1yh68aSCb7CvHIq1FqQe1UE_L5rFS0N1ia6H_3sw-uip68LJL2JlAvk0yk0m-CcAFE5SqhCNFOcRolQiIZMKQQBrKecIDoXBHd3QfDMfe7cSfNDzu4rB7vSNZTNQN1435nBFc7aBbwom3CW10HrArj1lvHVihHC-PQLcXc7URJjxRkWV-r-a7QWq8zB8bo4W9GezCTuUoOr3yz-7Bhsn2YftL-kBbGq1zrs4P4OFx-oIcY6uUZNqZ5a-rqpjbaeGt4ls6y2nilASWpXEwtJvPVqUCdiIrjeSsSvgQxoP-0_WQVDcmEGWH0oLYBsnUM3YJ4lOulHBNpGXqRqF90EhqTrVWJhLSvgPFtUoTHTAplAqp0qnkR9DK8swcg6Opm1p4qSsj1wsTnijJrRqzNs9TIZcduKxhi2dlYoy4SYGMIMcW5LgAOfY60K2RjatBMo-tkB-FmICsA1c12s3nv2s7-Z_4KWwxPIlSxE660Fq8f5gz60os5Dm0ezfPd_3zogt9AirrwZA |
| link.rule.ids | 315,786,790,27957,27958,41116,41558,42185,42627,52146,52269 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NS8MwFA86D-pB_MTp1B68aSBNurY5DnFM3XbQDXYLzUdF0Ha4Odh_b16brip68NIS-l4gr0ney0t-vyB0STkhKmEAUY4gW8VDLCk3OJSGMJawkCvY0R0Mw944uJ-0Jw4UNqtOu1dbksVMXYPdaJtRDMsdiEsYDtbRBvCpw5JrTDurzAphcHsExL1A1oYpD7hDy_xezXePVIeZP3ZGC4fT3UU7LlL0OuWv3UNrJttH21_4A21psCJdnR2gx6eXZwAZW6Uk0940f126Ym7nhTcHuPQWL4lXIlgWxoPcbj5dlgrQi6w0oLOc8CEad29HNz3srkzAyo6lObYNkmlg7BqkTZhS3DexlqkfR_ZBYqkZ0VqZmEv7DhXTKk10SCVXKiJKp5IdoUaWZ-YYeZr4qQ3OiC9jP4gSlijJrBq1Ti9QEZNNdFWZTUxLZgxRcyCDkYU1siiMLIImalWWFW6UzIQVascRMJA10XVl7frz37Wd_E_8Am32RoO-6N8NH07RFoVjKUUipYUa8_cPc2bjirk8L7rRJ3CWw1c |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3JTsMwEB0BlRAc2BGFAjlwgxQnTpP4WAGlUFohFqmcongJQkBa0bRS-XrGTUIKggPiksjK2PIyjsfjec8ABzYjRIRUQ5Q97a1irsltpkyXK0JpSF0m9Iluu-M2753Lbq07heKfRLvnR5IppkGzNMXJcV9GxwXwza5R29RbH22jUNOZhZKD0xZ1vFQ_f2gVfhZC9V0S2grW1G2mzRyWYWd-Lujr-lQYnd_OSSfLT2MZwrziadTJc3WY8Kp4_8bp-J-WrcBSZpsa9VSZVmFGxWuwOMVYiKn2J83rYB1ubp8eNawZM4WxNPq9l3GW7OGf6DWDeBqjp9BIMTMjZWhvcq8_TjNovUVpjQfLhDfgvnF2d9I0s0saTIGzNzGxjjxyFO56aoQKwSzlSx5ZvocP4nNJiZRC-Yzj2xVUiiiUrs2ZEB4RMuJ0E-biXqy2wJDEitAcJBb3LccLaSg4xWw2LrOO8Cgvw2E-NEE_5eIICtZl3W8B9lsw6bfAKUMlH70gm5eDAIVqvqc5z8pwlA9G8fn30rb_Jr4P89enjeDqotPagQVbx8FMPDcVmEvehmoXDZmE72W6-gG2seka |
| 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=Signomial+and+polynomial+optimization+via+relative+entropy+and+partial+dualization&rft.jtitle=Mathematical+programming+computation&rft.au=Murray%2C+Riley&rft.au=Chandrasekaran%2C+Venkat&rft.au=Wierman%2C+Adam&rft.date=2021-06-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=1867-2949&rft.eissn=1867-2957&rft.volume=13&rft.issue=2&rft.spage=257&rft.epage=295&rft_id=info:doi/10.1007%2Fs12532-020-00193-4&rft.externalDocID=10_1007_s12532_020_00193_4 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1867-2949&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1867-2949&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1867-2949&client=summon |