-
Previous Article
Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities
- JIMO Home
- This Issue
-
Next Article
On the Levenberg-Marquardt methods for convex constrained nonlinear equations
An outcome space algorithm for minimizing the product of two convex functions over a convex set
1. | School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, N01 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam, Vietnam, Vietnam |
References:
[1] |
H. P. Benson and G. M. Boger, Multiplicative programming problems: Analysis and efficient point search heuristic,, Journal of Optimization Theory and Applications, 94 (1997), 487.
doi: 10.1023/A:1022600232285. |
[2] |
H. P. Benson and G. M. Boger, Outcome-space cutting-plane algorithm for linear multiplicative programming,, Journal of Optimization Theory and Applications, 104 (2000), 301.
doi: 10.1023/A:1004657629105. |
[3] |
H. P. Benson, An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming,, Journal of Global Optimization, 15 (1999), 315.
doi: 10.1023/A:1008316429329. |
[4] |
Y. Gao, G. Wu and W. Ma, A new global optimization approach for convex multiplicative programming,, Applied Mathematics and Computation, 216 (2010), 1206.
doi: 10.1016/j.amc.2010.02.012. |
[5] |
R. Hosrt, N. V. Thoai and J. Devries, On finding the new vertices and redundant constraints in cutting plane algorithms for global optimization,, Operations Research Letters, 7 (1988), 85.
doi: 10.1016/0167-6377(88)90071-5. |
[6] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, Journal of Global Optimization, 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[7] |
N. T. B. Kim, Finite algorithm for minimizing the product of two linear functions over a polyhedron,, Journal Industrial and Management Optimization, 3 (2007), 481.
doi: 10.3934/jimo.2007.3.481. |
[8] |
N. T. B. Kim, N. T. L. Trang and T. T. H. Yen, Outcome-space outer approximation algorithm for linear multiplicative programming,, East West Journal of Mathematics, 9 (2007), 81.
|
[9] |
H. Konno and T. Kuno, Linear multiplicative programming,, Mathematical Programming, 56 (1992), 51.
doi: 10.1007/BF01580893. |
[10] |
H. Konno and T. Kuno, Multiplicative programming problems,, Handbook of Global Optimization, (1995), 369.
|
[11] |
D. T. Luc, "Theory of Vector Optimization,", Springer-Verlag, (1989).
doi: 10.1007/978-3-642-50280-4. |
[12] |
T. Matsui, NP-hardness of linear multiplicative programming and related problems,, Journal of Global Optimization, 9 (1996), 113.
doi: 10.1007/BF00121658. |
[13] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optimization, 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[14] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam Journal of Mathematics, 33 (2005), 463.
|
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
T. V. Thieu, A finite method for globally minimizing concave function over unbounded polyhedral convex sets and its applications,, Acta Mathematica Hungarica, 52 (1988), 21.
doi: 10.1007/BF01952475. |
[17] |
N. V. Thoai, A global optimization approach for solving the convex multiplicative programming problem,, Journal of Global Optimization, 1 (1991), 341.
doi: 10.1007/BF00130830. |
[18] |
P. L. Yu, "Multiple-Criteria Decision Making,", Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
show all references
References:
[1] |
H. P. Benson and G. M. Boger, Multiplicative programming problems: Analysis and efficient point search heuristic,, Journal of Optimization Theory and Applications, 94 (1997), 487.
doi: 10.1023/A:1022600232285. |
[2] |
H. P. Benson and G. M. Boger, Outcome-space cutting-plane algorithm for linear multiplicative programming,, Journal of Optimization Theory and Applications, 104 (2000), 301.
doi: 10.1023/A:1004657629105. |
[3] |
H. P. Benson, An outcome space branch and bound-outer approximation algorithm for convex multiplicative programming,, Journal of Global Optimization, 15 (1999), 315.
doi: 10.1023/A:1008316429329. |
[4] |
Y. Gao, G. Wu and W. Ma, A new global optimization approach for convex multiplicative programming,, Applied Mathematics and Computation, 216 (2010), 1206.
doi: 10.1016/j.amc.2010.02.012. |
[5] |
R. Hosrt, N. V. Thoai and J. Devries, On finding the new vertices and redundant constraints in cutting plane algorithms for global optimization,, Operations Research Letters, 7 (1988), 85.
doi: 10.1016/0167-6377(88)90071-5. |
[6] |
B. Jaumard, C. Meyer and H. Tuy, Generalized convex multiplicative programming via quasiconcave minimization,, Journal of Global Optimization, 10 (1997), 229.
doi: 10.1023/A:1008203116882. |
[7] |
N. T. B. Kim, Finite algorithm for minimizing the product of two linear functions over a polyhedron,, Journal Industrial and Management Optimization, 3 (2007), 481.
doi: 10.3934/jimo.2007.3.481. |
[8] |
N. T. B. Kim, N. T. L. Trang and T. T. H. Yen, Outcome-space outer approximation algorithm for linear multiplicative programming,, East West Journal of Mathematics, 9 (2007), 81.
|
[9] |
H. Konno and T. Kuno, Linear multiplicative programming,, Mathematical Programming, 56 (1992), 51.
doi: 10.1007/BF01580893. |
[10] |
H. Konno and T. Kuno, Multiplicative programming problems,, Handbook of Global Optimization, (1995), 369.
|
[11] |
D. T. Luc, "Theory of Vector Optimization,", Springer-Verlag, (1989).
doi: 10.1007/978-3-642-50280-4. |
[12] |
T. Matsui, NP-hardness of linear multiplicative programming and related problems,, Journal of Global Optimization, 9 (1996), 113.
doi: 10.1007/BF00121658. |
[13] |
L. D. Muu and B. T. Tam, Minimizing the sum of a convex function and the product of two affine functions over a convex set,, Optimization, 24 (1992), 57.
doi: 10.1080/02331939208843779. |
[14] |
H. X. Phu, On efficient sets in $\mathbbR^2$,, Vietnam Journal of Mathematics, 33 (2005), 463.
|
[15] |
R. T. Rockafellar, "Convex Analysis,", Princeton University Press, (1970).
|
[16] |
T. V. Thieu, A finite method for globally minimizing concave function over unbounded polyhedral convex sets and its applications,, Acta Mathematica Hungarica, 52 (1988), 21.
doi: 10.1007/BF01952475. |
[17] |
N. V. Thoai, A global optimization approach for solving the convex multiplicative programming problem,, Journal of Global Optimization, 1 (1991), 341.
doi: 10.1007/BF00130830. |
[18] |
P. L. Yu, "Multiple-Criteria Decision Making,", Plenum Press, (1985).
doi: 10.1007/978-1-4684-8395-6. |
[1] |
Deren Han, Zehui Jia, Yongzhong Song, David Z. W. Wang. An efficient projection method for nonlinear inverse problems with sparsity constraints. Inverse Problems & Imaging, 2016, 10 (3) : 689-709. doi: 10.3934/ipi.2016017 |
[2] |
Wei Liu, Pavel Krejčí, Guoju Ye. Continuity properties of Prandtl-Ishlinskii operators in the space of regulated functions. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3783-3795. doi: 10.3934/dcdsb.2017190 |
[3] |
Guido De Philippis, Antonio De Rosa, Jonas Hirsch. The area blow up set for bounded mean curvature submanifolds with respect to elliptic surface energy functionals. Discrete & Continuous Dynamical Systems - A, 2019, 39 (12) : 7031-7056. doi: 10.3934/dcds.2019243 |
[4] |
Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 |
[5] |
Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete & Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094 |
[6] |
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 |
[7] |
Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023 |
[8] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[9] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[10] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[11] |
M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072 |
[12] |
Marcelo Messias. Periodic perturbation of quadratic systems with two infinite heteroclinic cycles. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1881-1899. doi: 10.3934/dcds.2012.32.1881 |
[13] |
Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 |
[14] |
Olena Naboka. On synchronization of oscillations of two coupled Berger plates with nonlinear interior damping. Communications on Pure & Applied Analysis, 2009, 8 (6) : 1933-1956. doi: 10.3934/cpaa.2009.8.1933 |
[15] |
Carlos Gutierrez, Nguyen Van Chau. A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 397-402. doi: 10.3934/dcds.2007.17.397 |
[16] |
Bernold Fiedler, Carlos Rocha, Matthias Wolfrum. Sturm global attractors for $S^1$-equivariant parabolic equations. Networks & Heterogeneous Media, 2012, 7 (4) : 617-659. doi: 10.3934/nhm.2012.7.617 |
[17] |
Hildeberto E. Cabral, Zhihong Xia. Subharmonic solutions in the restricted three-body problem. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 463-474. doi: 10.3934/dcds.1995.1.463 |
[18] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[19] |
Lei Liu, Li Wu. Multiplicity of closed characteristics on $ P $-symmetric compact convex hypersurfaces in $ \mathbb{R}^{2n} $. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020378 |
[20] |
Michel Chipot, Mingmin Zhang. On some model problem for the propagation of interacting species in a special environment. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020401 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]