Abstract
This paper presents with elementary proofs some results on the directional derivative of the optimal value of a finite dimensional optimization problem with parameters.
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References
A. Ben-Tal, Second-order and related extremality conditions in nonlinear programming, J. Optim. Theory Appl. 31 (1980) 145–165.
A.V. Fiacco,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming (Academic Press, New York, 1983).
J. Gauvin, Directional derivative for the value function in mathematical programming, in:Nonsmooth Optimization and Related Topics, eds. F.H. Clarke, V.F. Dem'yanov and F. Giannessi (Plenum, New York and London, 1988) pp. 167–184.
J. Gauvin and R. Janin, Directional behaviour of optimal solutions in nonlinear mathematical programming, Math. Oper. Res. 13 (1988) 629–649.
J. Gauvin and J.W. Tolle, Differential stability in nonlinear programming, SIAM J. Control Optim. 15 (1977) 294–311.
B. Gollan, On the marginal function in nonlinear programming, Math. Oper. Res. 9 (1984) 208–221.
R.T. Rockafellar, Directional differentiability of the optimal value function in nonlinear programming problems, Math. Prog. Study 21 (1984) 213–226.
A. Shapiro, Sensitivity analysis of nonlinear programs and differentiability properties of metric projection, SIAM J. Control Optim. 26 (1988) 628–645.
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This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-9273.
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Gauvin, J., Janin, R. Directional derivative of the value function in parametric optimization. Ann Oper Res 27, 237–252 (1990). https://doi.org/10.1007/BF02055197
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DOI: https://doi.org/10.1007/BF02055197