Open Access
Issue |
RAIRO-Oper. Res.
Volume 56, Number 3, May-June 2022
|
|
---|---|---|
Page(s) | 1533 - 1552 | |
DOI | https://doi.org/10.1051/ro/2022061 | |
Published online | 16 June 2022 |
- K.P. Bennett, Global tree optimization: a non-greedy decision tree algorithm. Comput. Sci. Stat. 26 (1994) 156–160. [Google Scholar]
- H.P. Benson and G.M. Boger, Outcome-space cutting-plane algorithm for linear multiplicative programming. J. Optim. Theory App. 104 (2000) 301–322. [CrossRef] [Google Scholar]
- A. Cambini and L. Martein, Generalized Convexity and Optimization: Theory and Applications. Lecture Notes in Economics and Mathematical Systems. Springer (2009). [Google Scholar]
- R. Cambini and C. Sodini, On the minimization of a class of generalized linear functions on a flow polytope. Optimization 63 (2014) 1449–1464. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Chen and H. Jiao, A nonisolated optimal solution of general linear multiplicative programming problems. Comput. Oper. Res. 36 (2009) 2573–2579. [CrossRef] [MathSciNet] [Google Scholar]
- M.C. Dorneich and N.V. Sahinidis, Global optimization algorithms for chip design and compaction. Eng. Optim. 25 (1995) 131–154. [CrossRef] [Google Scholar]
- Y.L. Gao, C.X. Xu and Y.T. Yang, Outcome-space branch and bound algorithm for solving linear multiplicative programming. In: International Conference on Computational and Information Science. Springer, Berlin, Heidelberg (2005) pp. 675–681. [Google Scholar]
- Y. Gao, C. Xu and Y. Yang, An outcome-space finite algorithm for solving linear multiplicative programming. Appl. Math. Comput. 179 (2006) 494–505. [MathSciNet] [Google Scholar]
- H. Jiao, A branch and bound algorithm for globally solving a class of nonconvex programming problems. Nonlinear Anal. Theory Methods App. 70 (2009) 1113–1123. [CrossRef] [Google Scholar]
- H. Jiao and Y. Shang, Image space branch-reduction-bound algorithm for globally solving the sum of affine ratios problem. J. Comput. Math. (2022) in press. [Google Scholar]
- H.-W. Jiao and Y.-L. Shang, Two-level linear relaxation method for generalized linear fractional programming. J. Oper. Res. Soc. China (2022). DOI: 10.1007/s40305-021-00375-4. [Google Scholar]
- H. Jiao, S. Liu and, Y. Chen, Global optimization algorithm of a generalized linear multiplicative programming. J. Appl. Math. Comput. 40 (2012) 551–568. [CrossRef] [MathSciNet] [Google Scholar]
- H. Jiao, W. Wang, R. Chen, Y. Shang and J. Yin, An efficient outer space algorithm for generalized linear multiplicative programming problem. IEEE Access 8 (2020) 80629–80637. [CrossRef] [Google Scholar]
- H. Jiao, Y. Shang and R. Chen, A potential practical algorithm for minimizing the sum of affine fractional functions. Optimization (2022). DOI: 10.1080/02331934.2022.2032051. [Google Scholar]
- H. Jiao, J. Ma and Y. Shang, Image space branch-and-bound algorithm for globally solving minimax linear fractional programming problem. Pac. J. Optim. 18 (2022) 195–212. [Google Scholar]
- H. Jiao, Y. Shang and W. Wang, Solving generalized polynomial problem by using new affine relaxed technique. Int. J. Comput. Math. 99 (2022) 309–331. [CrossRef] [MathSciNet] [Google Scholar]
- H.W. Jiao, W.J. Wang and P.P. Shen, Piecewise linear relaxation method for globally solving a class of multiplicative problems. Pac. J. Optim. (2022) in press. [Google Scholar]
- A. Khajavirad and N.V. Sahinidis, A hybrid LP/NLP paradigm for global optimization relaxations. Math. Prog. Comput. 10 (2018) 383–421. [CrossRef] [Google Scholar]
- H. Konno, H. Shirakawa and H. Yamazaki, A mean-absolute deviation-skewness portfolio optimization model. Ann. Oper. Res. 45 (1993) 205–220. [CrossRef] [MathSciNet] [Google Scholar]
- T. Kuno, A finite branch-and-bound algorithm for linear multiplicative programming. Comput. Optim. App. 20 (2001) 119–135. [CrossRef] [Google Scholar]
- T. Kuno, Y. Yajima and H. Konno, An outer approximation method for minimizing the product of several convex functions on a convex set. J. Global Optim. 3 (1993) 325–335. [CrossRef] [MathSciNet] [Google Scholar]
- S. Liu and Y. Zhao, An efficient algorithm for globally solving generalized linear multiplicative programming. J. Comput. Appl. Math. 296 (2016) 840–847. [CrossRef] [MathSciNet] [Google Scholar]
- X. Liu, T. Umegaki and Y. Yamamoto, Heuristic methods for linear multiplicative programming. J. Global Optim. 15 (1999) 433–447. [CrossRef] [MathSciNet] [Google Scholar]
- C.D. Maranas, I.P. Androulakis, C.A. Floudas, A.J. Berger and J.M. Mulvey, Solving long-term financial planning problems via global optimization. J. Econ. Dyn. Control 21 (1997) 1405–1425. [CrossRef] [Google Scholar]
- T. Matsui, NP-hardness of linear multiplicative programming and related problem. J. Global Optim. 9 (1996) 113–119. [CrossRef] [MathSciNet] [Google Scholar]
- J.M. Mulvey, R.J. Vanderbei and S.A. Zenios, Robust optimization of large-scale systems. Oper. Res. 43 (1995) 264–281. [Google Scholar]
- H.S. Ryoo and N.V. Sahinidis, Global optimization of multiplicative programs. J. Global Optim. 26 (2003) 387–418. [CrossRef] [MathSciNet] [Google Scholar]
- P. Shen and B. Huang, Global algorithm for solving linear multiplicative programming problems. Optim. Lett. 14 (2020) 693–710. [CrossRef] [MathSciNet] [Google Scholar]
- P. Shen, X. Bai and W. Li, A new accelerating method for globally solving a class of nonconvex programming problems. Nonlinear Anal. Theory Methods App. 71 (2009) 2866–2876. [CrossRef] [Google Scholar]
- P. Shen, K. Wang and T. Lu, Outer space branch and bound algorithm for solving linear multiplicative programming problems. J. Optim. 78 (2020) 453–482. [Google Scholar]
- P. Shen, K. Wang and T. Lu, Global optimization algorithm for solving linear multiplicative programming problems. Optimization (2020). DOI: 10.1080/02331934.2020.1812603. [Google Scholar]
- N.V. Thoai, A global optimization approach for solving the convex multiplicative programming problems. J. Global Optim. 1 (1991) 341–357. [CrossRef] [MathSciNet] [Google Scholar]
- C.F. Wang and S.Y. Liu, A new linearization method for generalized linear multiplicative programming. Comput. Oper. Res. 38 (2011) 1008–1013. [CrossRef] [MathSciNet] [Google Scholar]
- C.F. Wang, S.Y. Liu and P.P. Shen, Global minimization of a generalized linear multiplicative programming. Appl. Math. Modell. 36 (2012) 2446–2451. [CrossRef] [Google Scholar]
- C.F. Wang, Y.Q. Bai and P.P. Shen, A practicable branch-and-bound algorithm for globally solving multiplicative programming. Optimization 66 (2017) 397–405. [CrossRef] [MathSciNet] [Google Scholar]
- L.P. Yang, P.P. Shen and Y.G. Pei, A global optimization approach for solving generalized nonlinear multiplicative programming problem, In: Abstract Applied Analysis. Hindawi (2014). DOI: 10.1155/2014/641909. [Google Scholar]
- Y.F. Zhao and S.Y. Liu, An efficient method for generalized linear multiplicative programming problem with multiplicative constraints. SpringerPlus 5 (2016) 1–14. [CrossRef] [PubMed] [Google Scholar]
- Y.F. Zhao and T. Zhao, Global optimization for generalized linear multiplicative programming using convex relaxation. Math. Prob. Eng. (2018). DOI: 10.1155/2018/9146309. [Google Scholar]
- B. Zhang, Y. Gao, X. Liu and X. Huang, Output-space branch-and-bound reduction algorithm for a class of linear multiplicative programs. Mathematics 8 (2020) 315. [CrossRef] [Google Scholar]
- B. Zhang, Y. Gao and X. Liu, An efficient polynomial time algorithm for a class of generalized linear multiplicative programs with positive exponents. Math. Prob. Eng. 2021 (2021). DOI: 10.1155/2021/8877037. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.