# Two characterizations of Pareto minima in convex multicriteria optimization

Aplikace matematiky (1984)

- Volume: 29, Issue: 5, page 342-349
- ISSN: 0862-7940

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topZlobec, Sanjo. "Two characterizations of Pareto minima in convex multicriteria optimization." Aplikace matematiky 29.5 (1984): 342-349. <http://eudml.org/doc/15365>.

@article{Zlobec1984,

abstract = {Two conditions are given 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 characterizations of properly efficient and weakly efficient points of Karlin and Geoffrion.},

author = {Zlobec, Sanjo},

journal = {Aplikace matematiky},

keywords = {optimality conditions; properly efficient point; weakly efficient point; characterization of optimality; convex multicriteria optimization; global Pareto minimum; restricted Lagrangian; optimality conditions; properly efficient point; weakly efficient point; characterization of optimality; convex multicriteria optimization; global Pareto minimum; restricted Lagrangian},

language = {eng},

number = {5},

pages = {342-349},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Two characterizations of Pareto minima in convex multicriteria optimization},

url = {http://eudml.org/doc/15365},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Zlobec, Sanjo

TI - Two characterizations of Pareto minima in convex multicriteria optimization

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 5

SP - 342

EP - 349

AB - Two conditions are given 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 characterizations of properly efficient and weakly efficient points of Karlin and Geoffrion.

LA - eng

KW - optimality conditions; properly efficient point; weakly efficient point; characterization of optimality; convex multicriteria optimization; global Pareto minimum; restricted Lagrangian; optimality conditions; properly efficient point; weakly efficient point; characterization of optimality; convex multicriteria optimization; global Pareto minimum; restricted Lagrangian

UR - http://eudml.org/doc/15365

ER -

## References

top- R. Abrams L. Kerzner, 10.1007/BF00933262, Journal of Optimization Theory and Applications 25 (1978), 161-170. (1978) MR0484413DOI10.1007/BF00933262
- A. Ben-Israel, 10.1016/0022-247X(69)90054-7, Journal of Mathematical Analysis and Applications 27 (1969), 367-389. (1969) Zbl0174.31502MR0242865DOI10.1016/0022-247X(69)90054-7
- A. Ben-Israel A. Ben-Tal A. Charnes, 10.2307/1912673, Econometrica 45 (1977), 811 - 820. (1977) MR0452684DOI10.2307/1912673
- A. Ben-Israel A. Ben-Tal S. Zlobec, Optimality in Nonlinear Programming: A Feasible Directions Approach, Wiley-Interscience, New York, 1981. (1981) MR0607673
- A. Ben-Tal A. Ben-Israel S. Zlobec, 10.1007/BF00933129, Journal cf Optimization Theory and Applications 20 (1976), 417-437. (1976) MR0439190DOI10.1007/BF00933129
- 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. (1979) MR0552107
- Y. Censor, 10.1007/BF01442131, Applied Mathematics and Optimization 4 (1977), 41 - 59. (1977) MR0488732DOI10.1007/BF01442131
- A. Charnes W. W. Cooper, Management Models and Industrial Applications of Linear Programming, Vol. I. Wiley, New York, 1961. (1961) MR0157774
- A. M. Geoffrion, 10.1016/0022-247X(68)90201-1, Journal of Mathematical Analysis and Applications 22 (1968), 618 - 630. (1968) Zbl0181.22806MR0229453DOI10.1016/0022-247X(68)90201-1
- S. Karlin, Mathematical Methods and Theory in Games. Programming and Economics, Vol. I, Addison-Wesley, Reading, Massachussetts, 1959. (1959) MR1160778
- V. V. Podinovskii, Applying the procedure for maximizing the basic local criterion to solving the vector optimization problems, Systems Control 6, Novosibirsk, 1970 (In Russian). (1970)
- V. V. Podinovskii V. M. Gavrilov, Optimization with Respect to Successive Criteria, Soviet Radio, Moscow, 1975 (In Russian). (1975) MR0454779
- R. T. Rockafellar, Convex Analysis, Princeton University Press, 1970. (1970) Zbl0193.18401MR0274683
- M. E. Salukvadze, Vector-Valued Optimization Problems in Control Theory, Academic Press, New York, 1979. (1979) Zbl0471.49001MR0563922
- S. Smale, 10.1016/0304-4068(74)90002-0, Journal of Mathematical Economics 1 (1974), 107-117. (1974) Zbl0316.90007MR0426823DOI10.1016/0304-4068(74)90002-0
- S. Smale, 10.1016/0304-4068(74)90013-5, Journal of Mathematical Economics 1 (1974), 213-221. (1974) Zbl0357.90010MR0426826DOI10.1016/0304-4068(74)90013-5
- S. Smale, 10.1016/0304-4068(76)90002-1, Journal of Mathematical Economics 3 (1976), 1-14. (1976) Zbl0348.90017MR0426827DOI10.1016/0304-4068(76)90002-1
- S. Zlobec, Regions of stability for ill-posed convex programs, Aplikace Matematiky 27 (1982), 176-191. (1982) Zbl0482.90073MR0658001

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