The Fermat Rule and Lagrange Multiplier Rule for Various Efficient Solutions of Set-Valued Optimization Problems Expressed in Terms of Coderivatives

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Recently, the interest toward set-valued optimization problems, i.e., optimization problems with set-valued objective and/or constrain maps, has grown up. Exploiting advanced tools of variational analysis and set-valued analysis, the authors obtained a number of (necessary and/or sufficient) optimality conditions expressed in terms of generalized derivatives such as contingent derivative [ 2, 13, 62, 66], first-order derivative [14, 15], second-order derivative [ 28, 40], epiderivative and generalized epiderivative [10, 22, 24, 39, 43, 44], subgradient/subdifferential [4, 5, 39, 67] and coderivatives [ 2, 4, 5, 18, 27, 28, 29, 33, 39, 72, 73].