Approximation methods for non-convex curves

作者: Y. Liu , K.L. Teo , X.Q. Yang

DOI: 10.1016/S0377-2217(98)90203-X

关键词: Regular polygonRate of convergenceMathematicsEfficient frontierSpace (mathematics)Applied mathematicsMathematical optimizationOptimization problemBlock (data storage)

摘要: Based on the triangle sandwich and block methods, two approximation methods for non-convex curves are considered in this paper. Numerical algorithms corresponding to these developed quadratic convergence properties of original space established. Application is given an efficient frontier a bi-criteria optimization problem.

参考文章(11)
C. J. Goh, X. Q. Yang, Convexification of a Noninferior Frontier Journal of Optimization Theory and Applications. ,vol. 97, pp. 759- 768 ,(1998) , 10.1023/A:1022654528902
Rainer E. Burkard, Horst W. Hamacher, Günter Rote, Sandwich approximation of univariate convex functions with an application to separable convex programming Naval Research Logistics. ,vol. 38, pp. 911- 924 ,(1991) , 10.1002/NAV.3800380609
B. Fruhwirth, R.E. Bukkard, G. Rote, Approximation of convex curves with application to the bicriterial minimum cost flow problem European Journal of Operational Research. ,vol. 42, pp. 326- 338 ,(1989) , 10.1016/0377-2217(89)90443-8
M. BALACHANDRAN, J. S. GERO, A COMPARISON OF THREE METHODS FOR GENERATING THE PARETO OPTIMAL SET Engineering Optimization. ,vol. 7, pp. 319- 336 ,(1984) , 10.1080/03052158408960646
X.Q. Yang, C.J. Goh, A method for convex curve approximation European Journal of Operational Research. ,vol. 97, pp. 205- 212 ,(1997) , 10.1016/0377-2217(95)00368-1
D. Li, Convexification of a noninferior frontier Journal of Optimization Theory and Applications. ,vol. 88, pp. 177- 196 ,(1996) , 10.1007/BF02192028