On Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems. (English) Zbl 0831.49021

Consider the Pareto optimization problem \[ \min f(x)\quad\text{with} \quad x\in C\quad\text{and} \quad g(x)\in D,\tag{1} \] where \(f: E\to F\), \(g: E\to G\), \(E\), \(F\) and \(G\) are Banach spaces, \(C\) and \(D\) are nonempty subsets of \(E\) and \(G\), respectively.
L. Thibault [Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems (to appear)] has shown how to obtain for (1) the existence of multipliers from approximate subdifferential for composite functions. The author proves the same result but in a simpler way.


49J52 Nonsmooth analysis
90C29 Multi-objective and goal programming
65K05 Numerical mathematical programming methods
Full Text: DOI


[1] Thibault L., Lagrange-Kuhn-Tucker multipliers for Pareto optimization problems · Zbl 0771.90092
[2] DOI: 10.1007/BF00935364 · Zbl 0502.90076
[3] Clarke F. H., Optimization and Nonsmooth Analysis (1983) · Zbl 0582.49001
[4] DOI: 10.1080/01630568908816291 · Zbl 0688.35019
[5] DOI: 10.1080/02331939208843857 · Zbl 0817.90090
[6] DOI: 10.1112/S0025579300013541 · Zbl 0713.49022
[7] DOI: 10.1016/0021-8928(76)90136-2 · Zbl 0362.49017
[8] DOI: 10.1007/BF01789411 · Zbl 0486.46037
[9] Jurani A., the Bulletin of Australian Mathematical Society
[10] Hhlriart-Uruty J. B., Tangent cones, generalized gradients and mathematical programming in Banach spaces. (1978)
[11] DOI: 10.1137/0713043 · Zbl 0347.90050
[12] Aubin J. P., Set Valued Analysis (1990) · Zbl 0713.49021
[13] Bborwein J. M., Journal of Optimization Theory and Applications 48 pp 9– (1986)
[14] DOI: 10.1016/0362-546X(87)90073-3 · Zbl 0642.49010
[15] DOI: 10.1287/moor.18.2.390 · Zbl 0779.49021
[16] Mordukovich B. S., Approximation Methods in Problem of Optimization and Control (1988)
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