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October  2016, 12(4): 1417-1433. doi: 10.3934/jimo.2016.12.1417

Outcome space algorithm for generalized multiplicative problems and optimization over the efficient set

Tran Ngoc Thang 1, and  Nguyen Thi Bach Kim 1,

1. 

School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, No. 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam, Vietnam

Received  December 2014 Revised  June 2015 Published  January 2016

In this paper, an algorithm of the branch and bound type in outcome space is proposed for solving a global optimization problem that includes, as a special case, generalized multiplicative problems. As an application, we solve the problem of optimizing over the efficient set of a bicriteria concave maximization problem. Preliminary computational experiments show that this algorithm works well for problems where the dimensions of the decision space can be fairly large.
Keywords: Global optimization, outcome space, branch and bound., optimization over the efficient set, generalized multiplicative problem.
Mathematics Subject Classification: Primary: 90C29; Secondary: 90C2.
Citation: Tran Ngoc Thang, Nguyen Thi Bach Kim. Outcome space algorithm for generalized multiplicative problems and optimization over the efficient set. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1417-1433. doi: 10.3934/jimo.2016.12.1417
References:
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show all references

References:
[1]

J. Optim. Theory Appl., 149 (2011), 411-419. doi: 10.1007/s10957-010-9782-2.  Google Scholar

[2]

J. Global Optim., 3 (1993), 95-111. doi: 10.1007/BF01100242.  Google Scholar

[3]

J. Optim. Theory Appl., 88 (1996), 77-105. doi: 10.1007/BF02192023.  Google Scholar

[4]

J. Optim. Theory Appl., 137 (2008), 105-120. doi: 10.1007/s10957-007-9323-9.  Google Scholar

[5]

J. Optim. Theory Appl., 105 (2000), 37-54. doi: 10.1023/A:1004657827134.  Google Scholar

[6]

J. Optim. Theory Appl., 92 (1997), 605-631. doi: 10.1023/A:1022659523991.  Google Scholar

[7]

Eur. J. Oper. Res., 33 (1988), 91-97. doi: 10.1016/0377-2217(88)90257-3.  Google Scholar

[8]

J. Global Optim., 10 (1997), 229-256. doi: 10.1023/A:1008203116882.  Google Scholar

[9]

in Modelling, Computation and Optimization in Information Systems and Management Sciences (eds. L. T. H. An, P. Bouvry and P. D. Tao), Communications in Computer and Information Science, 14 (2008), 234-243. Google Scholar

[10]

Optim. 51 (2002), 401-421. doi: 10.1080/02331930290019486.  Google Scholar

[11]

Pacific J. Optim., 9 (2013), 103-115.  Google Scholar

[12]

J. Global Optim, 4 (1994), 47-62. doi: 10.1007/BF01096534.  Google Scholar

[13]

Springer-Verlag, Berlin, Germany, 1989.  Google Scholar

[14]

in Recent Advances in Optimization (eds. P. Gritzmann, R. Horst, E. Sachs and R. Tichatschke), Lecture Notes in Economics and Mathematical Systems, 452 (1997), 183-195. doi: 10.1007/978-3-642-59073-3_13.  Google Scholar

[15]

SIAM J. Optim., 15 (2005), 987-1001. doi: 10.1137/040603097.  Google Scholar

[16]

Optim., 24 (1992), 57-62. doi: 10.1080/02331939208843779.  Google Scholar

[17]

Vietnam J. Math., 33 (2005), 463-468.  Google Scholar

[18]

in Some Current Advanced Researches on Information and Computer Science in Vietnam, Advances in Intelligent Systems and Computing, 341 (2015), 31-47. doi: 10.1007/978-3-319-14633-1_3.  Google Scholar

[19]

J. Global Optim., 18 (2000), 321-336. doi: 10.1023/A:1026544116333.  Google Scholar

[20]

Kluwer Academic Publishers, 1998. doi: 10.1007/978-1-4757-2809-5.  Google Scholar

[21]

J. Global Optim., 22 (2002), 285-317. doi: 10.1023/A:1013875600711.  Google Scholar

[22]

Plenum Press, New York and London, 1985. doi: 10.1007/978-1-4684-8395-6.  Google Scholar

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