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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References:

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