Piecewise Linear Multicriteria Programs: The Continuous Case and Its Discontinuous Generalization
Author
Abstract
Suggested Citation
DOI: 10.1287/opre.1110.1014
Download full text from publisher
References listed on IDEAS
- Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
- Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.
- Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
- Beltran-Royo, C., 2007. "A conjugate Rosen's gradient projection method with global line search for piecewise linear concave optimization," European Journal of Operational Research, Elsevier, vol. 182(2), pages 536-551, October.
- Sven Leyffer, 2009. "A Complementarity Constraint Formulation of Convex Multiobjective Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 257-267, May.
- Holmberg, Kaj & Ling, Jonas, 1997. "A Lagrangean heuristic for the facility location problem with staircase costs," European Journal of Operational Research, Elsevier, vol. 97(1), pages 63-74, February.
- Ruud Heuts & Jan de Klein, 1995. "An (s, q) inventory model with stochastic and interrelated lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 839-859, August.
- Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2007. "Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs," Operations Research, INFORMS, vol. 55(1), pages 146-157, February.
- Kameshwaran, S. & Narahari, Y., 2009. "Nonconvex piecewise linear knapsack problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 56-68, January.
- Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
- Daniel Bienstock & Oktay Günlük, 1996. "Capacitated Network Design---Polyhedral Structure and Computation," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 243-259, August.
- X Cai & K L Teo & X Q Yang & X Y Zhou, 2004. "Minimax portfolio optimization: empirical numerical study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 65-72, January.
- X. Q. Yang & N. D. Yen, 2010. "Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 113-124, October.
- Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
- Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
- Holmberg, Kaj, 1994. "Solving the staircase cost facility location problem with decomposition and piecewise linearization," European Journal of Operational Research, Elsevier, vol. 75(1), pages 41-61, May.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Margarita M. L. Rodríguez & José Vicente-Pérez, 2017. "On Finite Linear Systems Containing Strict Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 131-154, April.
- Siming Pan & Shaokai Lu & Kaiwen Meng & Shengkun Zhu, 2021. "Trade-Off Ratio Functions for Linear and Piecewise Linear Multi-objective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 402-419, February.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Tue R. L. Christensen & Kim Allan Andersen & Andreas Klose, 2013. "Solving the Single-Sink, Fixed-Charge, Multiple-Choice Transportation Problem by Dynamic Programming," Transportation Science, INFORMS, vol. 47(3), pages 428-438, August.
- Ram Kumar P N, 2013. "On Modeling The Step Fixed-Charge Transportation Problem," Working papers 134, Indian Institute of Management Kozhikode.
- F. J. Hwang & Yao-Huei Huang, 2021. "An effective logarithmic formulation for piecewise linearization requiring no inequality constraint," Computational Optimization and Applications, Springer, vol. 79(3), pages 601-631, July.
- Jose L. Andrade-Pineda & David Canca & Pedro L. Gonzalez-R, 2017. "On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization," Annals of Operations Research, Springer, vol. 258(2), pages 301-346, November.
- Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2007. "Variable Disaggregation in Network Flow Problems with Piecewise Linear Costs," Operations Research, INFORMS, vol. 55(1), pages 146-157, February.
- Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
- He, Guang & Huang, Nan-jing, 2014. "A new particle swarm optimization algorithm with an application," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 521-528.
- Nowak, Maciek & Hewitt, Mike & Bachour, Hussam, 2019. "Mileage bands in freight transportation," European Journal of Operational Research, Elsevier, vol. 272(2), pages 549-564.
- Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
- F. Sibel Salman & R. Ravi & John N. Hooker, 2008. "Solving the Capacitated Local Access Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 243-254, May.
- Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
- Christensen, Tue R.L. & Labbé, Martine, 2015. "A branch-cut-and-price algorithm for the piecewise linear transportation problem," European Journal of Operational Research, Elsevier, vol. 245(3), pages 645-655.
- Ya Ping Fang & Nan Jing Huang & Xiao Qi Yang, 2012. "Local Smooth Representations of Parametric Semiclosed Polyhedra with Applications to Sensitivity in Piecewise Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 810-839, December.
- Ioannis Gamvros & Bruce Golden & S. Raghavan, 2006. "The Multilevel Capacitated Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 348-365, August.
- Esther Mohr & Robert Dochow, 2017. "Risk management strategies for finding universal portfolios," Annals of Operations Research, Springer, vol. 256(1), pages 129-147, September.
- Nicolas Andalaft & Pablo Andalaft & Monique Guignard & Adrian Magendzo & Alexis Wainer & Andres Weintraub, 2003. "A Problem of Forest Harvesting and Road Building Solved Through Model Strengthening and Lagrangean Relaxation," Operations Research, INFORMS, vol. 51(4), pages 613-628, August.
- Alejandro Montoya & Mario C. Vélez–Gallego & Juan G. Villegas, 2016. "Multi-product capacitated facility location problem with general production and building costs," Netnomics, Springer, vol. 17(1), pages 47-70, July.
- Naoto Katayama, 2017. "A Combined Matheuristic for the Piecewise Linear Multicommodity Network Flow Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-24, December.
- Sanjay Jena & Jean-François Cordeau & Bernard Gendron, 2015. "Modeling and solving a logging camp location problem," Annals of Operations Research, Springer, vol. 232(1), pages 151-177, September.
- Puneet Pasricha & Dharmaraja Selvamuthu & Guglielmo D’Amico & Raimondo Manca, 2020. "Portfolio optimization of credit risky bonds: a semi-Markov process approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-14, December.
More about this item
Keywords
multicriteria program; piecewise linear function; the structure of (weak) Pareto solution set; bi-criteria program; algorithm;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:60:y:2012:i:2:p:398-409. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.