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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.

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