Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems

Annals of Operations Research

Volumn 166, Issue 1, 2009, Pages 271-279

  Efremov, Roman V ^a   Kamenev, Georgy K ^b  

^a UNIVERSIDAD REY JUAN CARLOS   (Spain)

^b DORODNICYN COMPUTING CENTER   (Russian Federation)

Author keywords

Estimation refinement method; Feasible goals method; Multicriteria optimization; Polyhedral approximation

Indexed keywords

EID: 58149502533     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-008-0418-y     Document Type: Article

References (18)

1. Bushenkov, V. A., & Lotov, A. V. (1982). Methods for the construction and application of generalized reachable sets. Moscow: Computing Center of the USSR Academy of Sciences (in Russian).
2. O. L. Chernykh 1988 Construction of the convex hull of a finite set of points when the computations are approximate Computational Mathematics and Mathematical Physics 28 5 71 77
3. O. L. Chernykh 1995 Approximating the Pareto hull of a convex set by polyhedral sets Computational Mathematics and Mathematical Physics 35 8 1033 1039
4. Dietrich, J., Schumann, A. H., & Lotov, A. V. (2006). Workflow oriented participatory decision support for integrated river basin planning. In A. Castelletti & R. Soncini Sessa (Eds.), Topics on system analysis and integrated water resource management (pp. 207-221). Amsterdam: Elsevier.
5. R. V. Efremov G. K. Kamenev 2002 An a priori estimate for the asymptotic efficiency of a class of algorithms for the polyhedral approximation of convex bodies Computational Mathematics and Mathematical Physics 42 1 20 29
6. Efremov, R., Rios Insua, D., & Lotov, A. (2006). A framework for participatory group decision support over the Web based on Pareto frontier visualization, goal identification and arbitration. Rey Juan Carlos University technical reports on statistics and decision sciences.
7. S. Gass T. Saaty 1955 The computational algorithm for the parametric objective function Naval Research Logistics Quarterly 2 39
8. P. M. Gruber 1993 Asymptotic estimates for best and stepwise approximation of convex bodies I Forum Mathematicum 5 281 297
9. G. K. Kamenev 1992 A class of adaptive algorithms for the approximation of bodies by polyhedra Computational Mathematics and Mathematical Physics 32 1 114 127
10. G. K. Kamenev 1994 Investigation of an algorithm for the approximation of convex bodies Computational Mathematics and Mathematical Physics 34 4 521 528
11. Larichev, O. Cognitive validity in design of decision-aiding techniques. Journal of Multi-Criteria Decision Analysis 1(3) (1992).
12. Lotov, A. V., Bushenkov, V. A., & Kamenev, G. K. (2004a). Interactive decision maps. Approximation and visualization of Pareto frontier. Dordrecht: Kluwer Academic.
13. Lotov, A., Kistanov, A., & Zaitsev, A. (2004b). Visualization-based data mining tool and its Web application. In Y. Shi, W. Xu, & Z. Chen (Eds.), Lecture notes in artificial intelligence (Vol. 3327(XIII), p. 263). Berlin/Heidelberg: Springer.
14. McMullen, P., & Shephard, G. C. (1971). Convex polytopes and the upper bound conjecture. Cambridge: Cambridge University Press.
15. Preparata, F. P., & Shamos, M. I. (1985). Computational geometry: An introduction. New York: Springer.
16. R. Schneider 1983 Zur optimalen Approximation konvexer Hyperflächen durch Polyeder Mathematische Annalen 256 3 289 301
17. R. Schneider J. A. Wieacker 1981 Approximation of convex bodies by polytopes Bulletin of the London Mathematical Society 13 149 156
18. Wierzbicki, A. (1981). A mathematical basis for satisfying decision making. In J. Morse (Ed.), Organizations: Multiple agents with multiple criteria (pp. 465-485). Berlin: Springer.