-
Previous Article
Theory and applications of optimal control problems with multiple time-delays
- JIMO Home
- This Issue
-
Next Article
Optimizing system-on-chip verifications with multi-objective genetic evolutionary algorithms
A ladder method for linear semi-infinite programming
1. | School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia, Australia |
References:
[1] |
E. J. Anderson and A. S. Lewis, An extension of the simplex algorithm for semi-infinite linear programming,, Mathematical Programming, 44 (1989), 247.
doi: 10.1007/BF01587092. |
[2] |
B. Betrò, An accelerated central cutting plane algorithm for semi-infinite linear programming,, Mathematical Programming, 101 (2004), 479.
doi: 10.1007/s10107-003-0492-5. |
[3] |
D. den Hertog, J. Kaliski, C. Roos and T. Terlaky, A logarithmic barrier cutting plane method for convex programming,, Annals of Operations Research, 58 (1995), 69.
doi: 10.1007/BF02032162. |
[4] |
M. C. Ferris and A. B. Philpott, An interior point algorithm for semi-infinite linear programming,, Mathematical Programming, 43 (1989), 257.
doi: 10.1007/BF01582293. |
[5] |
M. A. Goberna and M. A. López, Linear Semi-infinite Optimization,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[6] |
M. A. Goberna, Linear semi-infinite optimization: Recent advances,, in Continuous Optimization (eds. V. Jeyakumar and A. M. Rubinov), (2005), 3.
doi: 10.1007/0-387-26771-9_1. |
[7] |
R. Hettich, A review of numerical methods for semi-infinite optimization,, in Semi-infinite Programming and Applications (eds. A. V. Fiacco and K. O. Kortanek), (1983), 158.
doi: 10.1007/978-3-642-46477-5_11. |
[8] |
R. Hettich, An implementation of a discretization method for semi-infinite programming,, Mathematical Programming, 34 (1986), 354.
doi: 10.1007/BF01582235. |
[9] |
R. Hettich and K. O. Kortanek, Semi-infinite programming: Theory, methods, and applications,, SIAM Rev., 35 (1993), 380.
doi: 10.1137/1035089. |
[10] |
S. Ito, Y. Liu and K. L. Teo, A dual parametrization method for convex semi-infinite programming,, Ann. Oper. Res., 98 (2000), 189.
doi: 10.1023/A:1019208524259. |
[11] |
A. Kaplan and R. Tichatschke, Proximal interior point method for convex semi-infinite programming,, Optim. Methods Softw., 15 (2001), 87.
doi: 10.1080/10556780108805813. |
[12] |
Y. Liu, An exterior point method for linear programming based on inclusive normal cones,, J. Ind. Manag. Optim., 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[13] |
Y. Liu, Duality theorem in linear programming: From trichotomy to quadrichotomy,, J. Ind. Manag. Optim., 7 (2011), 1003.
doi: 10.3934/jimo.2011.7.1003. |
[14] |
Y. Liu and K. L. Teo, A bridging method for global optimization,, J. Austral. Math. Soc. Ser. B, 41 (1999), 41.
doi: 10.1017/S0334270000011024. |
[15] |
Y. Liu, K. L. Teo and S. Y. Wu, A New quadratic semi-infinite programming algorithm based on dual parametrization,, J. Global Optim., 29 (2004), 401.
doi: 10.1023/B:JOGO.0000047910.80739.95. |
[16] |
R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems,, J. Optim. Theory Appl., 71 (1991), 85.
doi: 10.1007/BF00940041. |
[17] |
G. A. Watson, Lagrangian methods for semi-infinite programming problems,, in Infinite Programming, (1985), 90.
doi: 10.1007/978-3-642-46564-2_8. |
[18] |
S. Y. Wu, S. C. Fang and C. J. Lin, Relaxed cutting plane method for solving linear semi-infinite programming problems,, J. Optim. Theory Appl., 99 (1998), 759.
doi: 10.1023/A:1021763419562. |
show all references
References:
[1] |
E. J. Anderson and A. S. Lewis, An extension of the simplex algorithm for semi-infinite linear programming,, Mathematical Programming, 44 (1989), 247.
doi: 10.1007/BF01587092. |
[2] |
B. Betrò, An accelerated central cutting plane algorithm for semi-infinite linear programming,, Mathematical Programming, 101 (2004), 479.
doi: 10.1007/s10107-003-0492-5. |
[3] |
D. den Hertog, J. Kaliski, C. Roos and T. Terlaky, A logarithmic barrier cutting plane method for convex programming,, Annals of Operations Research, 58 (1995), 69.
doi: 10.1007/BF02032162. |
[4] |
M. C. Ferris and A. B. Philpott, An interior point algorithm for semi-infinite linear programming,, Mathematical Programming, 43 (1989), 257.
doi: 10.1007/BF01582293. |
[5] |
M. A. Goberna and M. A. López, Linear Semi-infinite Optimization,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[6] |
M. A. Goberna, Linear semi-infinite optimization: Recent advances,, in Continuous Optimization (eds. V. Jeyakumar and A. M. Rubinov), (2005), 3.
doi: 10.1007/0-387-26771-9_1. |
[7] |
R. Hettich, A review of numerical methods for semi-infinite optimization,, in Semi-infinite Programming and Applications (eds. A. V. Fiacco and K. O. Kortanek), (1983), 158.
doi: 10.1007/978-3-642-46477-5_11. |
[8] |
R. Hettich, An implementation of a discretization method for semi-infinite programming,, Mathematical Programming, 34 (1986), 354.
doi: 10.1007/BF01582235. |
[9] |
R. Hettich and K. O. Kortanek, Semi-infinite programming: Theory, methods, and applications,, SIAM Rev., 35 (1993), 380.
doi: 10.1137/1035089. |
[10] |
S. Ito, Y. Liu and K. L. Teo, A dual parametrization method for convex semi-infinite programming,, Ann. Oper. Res., 98 (2000), 189.
doi: 10.1023/A:1019208524259. |
[11] |
A. Kaplan and R. Tichatschke, Proximal interior point method for convex semi-infinite programming,, Optim. Methods Softw., 15 (2001), 87.
doi: 10.1080/10556780108805813. |
[12] |
Y. Liu, An exterior point method for linear programming based on inclusive normal cones,, J. Ind. Manag. Optim., 6 (2010), 825.
doi: 10.3934/jimo.2010.6.825. |
[13] |
Y. Liu, Duality theorem in linear programming: From trichotomy to quadrichotomy,, J. Ind. Manag. Optim., 7 (2011), 1003.
doi: 10.3934/jimo.2011.7.1003. |
[14] |
Y. Liu and K. L. Teo, A bridging method for global optimization,, J. Austral. Math. Soc. Ser. B, 41 (1999), 41.
doi: 10.1017/S0334270000011024. |
[15] |
Y. Liu, K. L. Teo and S. Y. Wu, A New quadratic semi-infinite programming algorithm based on dual parametrization,, J. Global Optim., 29 (2004), 401.
doi: 10.1023/B:JOGO.0000047910.80739.95. |
[16] |
R. Reemtsen, Discretization methods for the solution of semi-infinite programming problems,, J. Optim. Theory Appl., 71 (1991), 85.
doi: 10.1007/BF00940041. |
[17] |
G. A. Watson, Lagrangian methods for semi-infinite programming problems,, in Infinite Programming, (1985), 90.
doi: 10.1007/978-3-642-46564-2_8. |
[18] |
S. Y. Wu, S. C. Fang and C. J. Lin, Relaxed cutting plane method for solving linear semi-infinite programming problems,, J. Optim. Theory Appl., 99 (1998), 759.
doi: 10.1023/A:1021763419562. |
[1] |
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 |
[2] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[3] |
Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 |
[4] |
Seung-Yeal Ha, Myeongju Kang, Bora Moon. Collective behaviors of a Winfree ensemble on an infinite cylinder. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2749-2779. doi: 10.3934/dcdsb.2020204 |
[5] |
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 |
[6] |
Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781 |
[7] |
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 |
[8] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[9] |
Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 |
[10] |
Nizami A. Gasilov. Solving a system of linear differential equations with interval coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2739-2747. doi: 10.3934/dcdsb.2020203 |
[11] |
Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119 |
[12] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[13] |
Arunima Bhattacharya, Micah Warren. $ C^{2, \alpha} $ estimates for solutions to almost Linear elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021024 |
[14] |
Misha Bialy, Andrey E. Mironov. Rich quasi-linear system for integrable geodesic flows on 2-torus. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 81-90. doi: 10.3934/dcds.2011.29.81 |
[15] |
Fumihiko Nakamura. Asymptotic behavior of non-expanding piecewise linear maps in the presence of random noise. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2457-2473. doi: 10.3934/dcdsb.2018055 |
[16] |
Hirofumi Notsu, Masato Kimura. Symmetry and positive definiteness of the tensor-valued spring constant derived from P1-FEM for the equations of linear elasticity. Networks & Heterogeneous Media, 2014, 9 (4) : 617-634. doi: 10.3934/nhm.2014.9.617 |
[17] |
Jong Yoon Hyun, Yoonjin Lee, Yansheng Wu. Connection of $ p $-ary $ t $-weight linear codes to Ramanujan Cayley graphs with $ t+1 $ eigenvalues. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020133 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]