Abstract
First order optimality conditions with Lagrange multipliers for inquality constrained quasidifferentiable optimization are considered. Firstly, the advantage of Fritz John necessary of the optimality condition in terms of quasidifferential over that in terms of the Clarke generalized gradient, is discussed. Also, two sufficient optimality conditions for quasidifferentiable optimization are proposed. Finally, a necessary optimality condition in terms of both the quasidifferential and the Clarke generalized gradient, is presented.
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References
Clarke, F.H. (1983), Optimization and Nonsmooth Analysis, John Wiley and Sons, New York.
Demyanov, V.F. and Rubinov, A.M. (1986), Quasidifferential Calculus, Optimization Software Inc., New York.
Demyanov, V.F. and Rubinov, A.M. (1995), Constructive Nonsmooth Analysis, Peter Lang, Frankfurt a/M.
Demyanov, V. F.(1986), Quasidifferentiable functions: necessary conditions and descent directions, Mathematical Programming Study, Vol. 29, pp.20–43.
Eppler, K. and Luderer, B. (1987), The Lagrange principle and quasidifferential calculus, Wiss. Z. d. TU Karl-Marx-Stadt, Vol. 29, No.2, pp. 187–192.
Gao, Y.(1990), A weak Fritz John condition for quasidifferentiable functions, Chinese J. Operations Research, Vol. 9, No. 2, pp. 43–44. (In Chinese)
Gao, Y. (1994), Fritz John conditions for a quasidifferentiable function subject to equality and inequality constraints, Applied Mathematics—J. Chinese Universities (Ser. A), Vol.9, No.3, pp. 329–334. (In Chinese)
Gao, Y. (1998), Demyanov’s difference of two sets and optimality conditions in Lagrange multiplier type for constrained quasidifferentiable optimization, Technical Reports of CORA’98, Dalian University of Technology, pp. 11–24.
Luderer, B. (1991), Directional derivative estimates for the optimal value function of a quasidifferentiable programming problem, Mathematical Programming, Vol. 51, No.3, pp.333–348.
Polyakova, L. N. (1986), On the minimization of a quasidifferentiable function subject to equality-type constraints, Mathematical Programming Study, Vol. 29, pp.44–55.
Rockafellar, R. T. (1970), Convex Analysis Princeton University Press, Princeton.
Shapiro, A. (1984), On optimality conditions in quasidifferentiable optimization, SIAM J. Control and Optimization, Vol. 22, No. 4, pp. 610–617.
Xia, Z. Q. (1990), Generalized Fritz John conditions for quasidifferentiable min-imization, in: Law, A. G. and Wang, C. L. ed, Approximation, Optimization and Computing, Elsevier Science Publisher B. V., North Holland, pp.325–327.
Yin, H. and Zhang, K. (1998), The Fritz John type conditions in quasidifferentiable programming with equality constraints and their sufficiency, Applied Mathematics—J. Chinese Universities (Ser. A), Vol. 13, No.l, pp. 99–104. (In Chinese)
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Gao, Y. (2000). Optimality Conditions with Lagrange Multipliers for Inequality Constrained Quasidifferentiable Optimization. In: Demyanov, V., Rubinov, A. (eds) Quasidifferentiability and Related Topics. Nonconvex Optimization and Its Applications, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3137-8_6
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DOI: https://doi.org/10.1007/978-1-4757-3137-8_6
Publisher Name: Springer, Boston, MA
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