Zlobec, Sanjo Two characterizations of Pareto minima in convex multicriteria optimization. (English) Zbl 0549.90085 Apl. Mat. 29, 342-349 (1984). Summary: We give two conditions, each of which is both necessary and sufficient for a point to be a global Pareto minimum. The first one is obtained by studying programs where each criterion appears as a single objective function, while the second one is given in terms of a ”restricted Lagrangian”. The conditions are compared with the familiar characterization of properly efficient and weakly efficient points of Karlin and Geoffrion. Cited in 4 Documents MSC: 90C31 Sensitivity, stability, parametric optimization 90C25 Convex programming Keywords:optimality conditions; properly efficient point; weakly efficient point; characterization of optimality; convex multicriteria optimization; global Pareto minimum; restricted Lagrangian PDF BibTeX XML Cite \textit{S. Zlobec}, Apl. Mat. 29, 342--349 (1984; Zbl 0549.90085) Full Text: EuDML OpenURL References: [1] R. Abrams L. Kerzner: A simplified test for optimality. Journal of Optimization Theory and Applications 25 (1978), 161-170. · Zbl 0352.90047 [2] A. Ben-Israel: Linear equations and inequalities on finite dimensional, real or complex, vector spaces: A unified theory. Journal of Mathematical Analysis and Applications 27 (1969), 367-389. · Zbl 0174.31502 [3] A. Ben-Israel A. Ben-Tal A. Charnes: Necessary and sufficient conditions for Pareto optimum in convex programming. Econometrica 45 (1977), 811 - 820. · Zbl 0367.90093 [4] A. Ben-Israel A. Ben-Tal S. Zlobec: Optimality in Nonlinear Programming: A Feasible Directions Approach. Wiley-Interscience, New York, 1981. · Zbl 0454.90043 [5] A. Ben-Tal A. Ben-Israel S. Zlobec: Characterization of optimality in convex programming without a constraint qualification. Journal cf Optimization Theory and Applications 20 (1976), 417-437. · Zbl 0327.90025 [6] G. R. Bitran T. L. Magnanti: The structure of admissible points with respect to cone dominance. Journal of Optimization Theory and Applications 29 (1979), 473 - 514. · Zbl 0389.52021 [7] Y. Censor: Pareto optimality in multiobjective problems. Applied Mathematics and Optimization 4 (1977), 41 - 59. · Zbl 0346.90055 [8] A. Charnes W. W. Cooper: Management Models and Industrial Applications of Linear Programming. Vol. I. Wiley, New York, 1961. · Zbl 0107.37004 [9] A. M. Geoffrion: Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications 22 (1968), 618 - 630. · Zbl 0181.22806 [10] S. Karlin: Mathematical Methods and Theory in Games. Programming and Economics. Vol. I, Addison-Wesley, Reading, Massachussetts, 1959. · Zbl 0139.12704 [11] V. V. Podinovskii: Applying the procedure for maximizing the basic local criterion to solving the vector optimization problems. Systems Control 6, Novosibirsk, 1970 [12] V. V. Podinovskii V. M. Gavrilov: Optimization with Respect to Successive Criteria. Soviet Radio, Moscow, 1975 [13] R. T. Rockafellar: Convex Analysis. Princeton University Press, 1970. · Zbl 0193.18401 [14] M. E. Salukvadze: Vector-Valued Optimization Problems in Control Theory. Academic Press, New York, 1979. · Zbl 0471.49001 [15] S. Smale: Global analysis and economics III. Journal of Mathematical Economics 1 (1974), 107-117. · Zbl 0316.90007 [16] S. Smale: Global analysis and economics V. Journal of Mathematical Economics 1 (1974), 213-221. · Zbl 0357.90010 [17] S. Smale: Global analysis and economics VI. Journal of Mathematical Economics 3 (1976), 1-14. · Zbl 0348.90017 [18] S. Zlobec: Regions of stability for ill-posed convex programs. Aplikace Matematiky 27 (1982), 176-191. · Zbl 0482.90073 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.