Lin, Z. H.; Zhu, D. L.; Sheng, Z. P. Finding a minimal efficient solution of a convex multiobjective program. (English) Zbl 1061.90102 J. Optimization Theory Appl. 118, No. 3, 587-600 (2003). Summary: We construct an interior-point homotopy method for solving a minimal efficient solution of a convex multiobjective program. Some examples are shown. Cited in 1 ReviewCited in 7 Documents MSC: 90C29 Multi-objective and goal programming 90C51 Interior-point methods Keywords:Convex multiobjective programs; minimal efficient solutions; interior-point methods; global convergence; parametrized Sard theorem PDF BibTeX XML Cite \textit{Z. H. Lin} et al., J. Optim. Theory Appl. 118, No. 3, 587--600 (2003; Zbl 1061.90102) Full Text: DOI OpenURL References: [1] Pareto, V., Course d’Economic Politique, Rouge, Lausanne, Switzerland, 1896. [2] Von Neumann, J., and Morgenstern, O., Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944. · Zbl 0063.05930 [3] Koopmans, T.C., Activity Analysis of Production and Allocation, Wiley, New York, NY, 1951. · Zbl 0045.09503 [4] Kostreva, M. M., and Wiecek, M.M., Linear Complementarity Problems and Multiple-Objective Programming, Mathematical Programming, Vol. 60, pp. 349-359, 1993. · Zbl 0796.90047 [5] Konno, H., and Kuno, T., Linear Multiple-Objective Linear Programming, Mathematical Programming, Vol. 56, pp. 51-64, 1992. · Zbl 0761.90080 [6] Isac, G., Kostreva, M. M., and Wiecek, M.M., Multiple-Objective Approximation of Feasible but Unsolvable Linear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 86, pp. 389-405, 1995. · Zbl 0838.90120 [7] Ecker, J. G., Hegner, N. S., and Kouada, I.A., Generating All Maximal Efficient Faces for Multiple-Objective Linear Programs, Journal of Optimization Theory and Applications, Vol. 30, pp. 353-381, 1980. · Zbl 0393.90087 [8] Armand, P., Finding All Maximal Efficient Faces in Multiobjective Linear Programming, Mathematical Programming, Vol. 61, pp. 357-375, 1993. · Zbl 0795.90054 [9] Megiddo, N., Editor, Progress in Mathematical Programming, Interior Point and Related Methods, Springer Verlag, New York, NY, 1988. [10] Lin, Z., Li, Y., and Yu, B., A Combined Homotopy Interior-Point Method for General Nonlinear Programming Problems, Applied Mathematics and Computation, Vol. 80, pp. 209-224, 1996. · Zbl 0883.65054 [11] Watson, L. T., Theory of Globally Convergent Probability-One Homotopies for Nonlinear Programming, SIAM Journal on Optimization, Vol. 11, pp. 761-780, 2000. · Zbl 0994.65070 [12] Chow, S.N., Mallet-Paret, J., and Yorke, J.A., Finding Zeros of Maps: Homotopy Methods That Are Constructive with Probability One, Mathematical Computation, Vol. 32, pp. 887-899, 1978. · Zbl 0398.65029 [13] Smale, S., AConvergent Process of Price Adjustment and Global Newton Method, Journal of Mathematical Economics, Vol. 3, pp. 1-14, 1976. · Zbl 0348.90017 [14] Allgower, E. L., and Georg, K., Numerical Continuation Methods: An Introduction, Springer Verlag, Berlin, Germany, 1990. · Zbl 0717.65030 [15] Naber, G. L., Topological Methods in Euclidean Space, Cambridge University Press, London, England, 1980. · Zbl 0437.55001 [16] Lin, Z., Yu, B., and Feng, G., A Combined Homotopy Interior-Point Method for Convex Nonlinear Programming Problems, Applied Mathematics and Computation, Vol. 84, pp. 193-211, 1997. · Zbl 0898.90100 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.