Global algorithm for a class of multiplicative programs using piecewise linear approximation technique
This paper presents an efficient algorithm for solving a class of multiplicative programs (MP). For obtaining the global optimal solution of the problem (MP), we first transform the problem (MP) into the equivalent problem (EP) by introducing auxiliary variables. Next, using the new piecewise linear...
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| Veröffentlicht in: | Numerical algorithms 2023-02, Vol.92 (2), p.1063-1082 |
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| container_title | Numerical algorithms |
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| creator | Hou, Zhisong Liu, Sanyang |
| description | This paper presents an efficient algorithm for solving a class of multiplicative programs (MP). For obtaining the global optimal solution of the problem (MP), we first transform the problem (MP) into the equivalent problem (EP) by introducing auxiliary variables. Next, using the new piecewise linear approximation technique, the problem (EP) is systematically converted into a series of linear relaxation programming problems (RP) for obtaining the lower bound of the optimal value for the problem (EP). Then, according to the characteristics of the problem (EP) and the structure of the branch-and-bound framework, some outer space accelerating techniques are constructed to improve the speed of the convergence of the algorithm. Furthermore, by analyzing the computational complexity of the algorithm, we give an estimation for the maximum iterations of the algorithm. Finally, numerical results are reported to demonstrate the effectiveness and robustness of the algorithm. |
| doi_str_mv | 10.1007/s11075-022-01330-x |
| format | Article |
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Finally, numerical results are reported to demonstrate the effectiveness and robustness of the algorithm.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Computer Science</subject><subject>Linear programming</subject><subject>Lower bounds</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Optimization</subject><subject>Original Paper</subject><subject>Robustness (mathematics)</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1PxCAQhonRxHX1D3gi8YwOIGU5mo2uJpt40TOhlHbZ0A-h1fXfi9bEm6eZw_O8M3kRuqRwTQHkTaIUpCDAGAHKOZDDEVpQIRlRrBDHeQcqCeVqdYrOUtoDZI3JBao3oS9NwCY0ffTjrsV1H7HBNpiUcF_jdgqjH4K3ZvTvDg-xb6JpE56S7xo8eGfdh08OB985k80hEwffZrrv8OjsrvNvkztHJ7UJyV38ziV6fbh_WT-S7fPmaX23JZZTNRLmmCqEqnjpXFEpJgrBhJQrySyvSqiMAa4E2IoaY6kpmATKGFUllEKWleFLdDXn5i_y2TTqfT_FLp_UTNFVAbK4ZZliM2Vjn1J0tR5ifjl-agr6u08996lzn_qnT33IEp-llOGucfEv-h_rC0y3eoc</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Hou, Zhisong</creator><creator>Liu, Sanyang</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0002-7415-7073</orcidid></search><sort><creationdate>20230201</creationdate><title>Global algorithm for a class of multiplicative programs using piecewise linear approximation technique</title><author>Hou, Zhisong ; Liu, Sanyang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-2e29659d3bee6d925652577872c3db0daa03950cd1aac1a627012219b0b57bda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Approximation</topic><topic>Computer Science</topic><topic>Linear programming</topic><topic>Lower bounds</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Optimization</topic><topic>Original Paper</topic><topic>Robustness (mathematics)</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hou, Zhisong</creatorcontrib><creatorcontrib>Liu, Sanyang</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hou, Zhisong</au><au>Liu, Sanyang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global algorithm for a class of multiplicative programs using piecewise linear approximation technique</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2023-02-01</date><risdate>2023</risdate><volume>92</volume><issue>2</issue><spage>1063</spage><epage>1082</epage><pages>1063-1082</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>This paper presents an efficient algorithm for solving a class of multiplicative programs (MP). 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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Algorithms Approximation Computer Science Linear programming Lower bounds Numeric Computing Numerical Analysis Optimization Original Paper Robustness (mathematics) Theory of Computation |
| title | Global algorithm for a class of multiplicative programs using piecewise linear approximation technique |
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