Abstract
In recent years an increasing attention has been devoted to the use of nondifferentiable exact penalty functions for the solution of nonlinear programming problems. However, as pointed out in [22], virtually all the published literature on exact penalty functions treats one of two cases: either the nonlinear programming problem is a convex problem (see, e.g., [2], [18], [23]), or it is a smooth problem (see, e.g., [1], [3–5], [10–13], [16], [18–20]). Exact penalty functions for nonlinear programming problems neither convex nor smooth, have been considered in [6], [21], [22], where locally lipschitz problems are dealt with.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.S. Bazaraa and J.J. Goode. “Sufficient conditions for a globally exact penalty function without convexity”. Math. Progr. Study, 19 (1982), pp. 1–15.
D.P. Bertsekas. “Necessary and sufficient conditions for a penalty method to be exact”. Math. Programming, 9 (1975), pp. 87–99.
D.P. Bertsekas. “Constrained optimization and Lagrange multiplier methods”. Academic Press, New York (1982).
C. Charalambous. “A lower bound for the controlling parameters of the exact penalty function”. Math. Programming, 15 (1978), pp. 278–290.
C. Charalambous. “On conditions for optimality of a class of nondifferentiable functions”. J. Optim. Theory Appl., 43 (1984), pp. 135–142.
F.H. Clarke. “Generalized gradients of Lipschitz functionals”. Mathematics Research Center, Technical Summary Report, University of Wisconsin, Madison, WI. 43 (1976), pp. 135–142.
F.H. Clarke. “Optimization and nonsmooth analysis”. J. Wiley, New York (1983).
G. Di Pillo and L. Grippo. “An exact penalty method with global convergence properties for nonlinear programming problems”. Math. Programming, 36 (1986), pp. 1–18.
G. Di Pillo and L. Grippo. “Globally exact nondifferentiable penalty functions”. Report 10. 87, Dipartimento di Informatica e Sistemistica, University of Rome “La Sapienza”, Rome (1987).
G. Di Pillo and L. Grippo. “On the exactness of a class of nondifferentiable penalty functions”. Jou. Optimization. Th. Appl., 57 (1988), pp. 397–408.
J.P. Evans, F.J. Gould and J.W. Tolle. “Exact penalty functions in nonlinear programming”. Math. Programming, 4 (1973), pp. 72–97.
R. Fletcher. “Practical methods of optimization”. Vol. 2, J. Wiley, New York (1981).
S.P. Han and O.L. Mangasarian. “Exact penalty functions in nonlinear programming”. Math. Programming, 17 (1979), pp. 251–269.
J.B. Hiriart-Urruty. “Refinements of necessary optimality conditions in nondifferentiable programming II”. Math. Prog. Study, 19 (1982), pp. 120–139.
R.A. Horn and C.A. Johnson. “Matrix analysis”. Cambridge University Press, Cambridge (1985).
S. Howe. “New conditions for the exactness of a simple penalty function”. SIAM J. Control, 11 (1973), pp. 378–381.
O.L. Mangasarian. “Nonlinear Programming”. McGraw-Hill, Inc., Cambridge (1969).
O.L. Mangasarian. “Sufficiency of exact penalty minimization”. SIAM J. Control Optim., 23 (1985), pp. 30–37.
T. Pietrzykowski. “An exact potential method for constrained maxima”. SIAM J. Numer. Anal., 6 (1969), pp. 299–304.
T. Pietrzykowski. “The potential method for conditional maxima in the locally compact metric spaces”. Numer. Math., 14 (1970), pp. 325–329.
E. Polak, D.Q. Mayne and Y. Wardi. “On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems”. SIAM J. Control Optim., 21 (1983), pp. 190–203.
E. Rosenberg. “Exact penalty functions and stability in locally Lipschitz programming”. Math. Programming, 30 (1984), pp. 340–356.
W.I. Zangwill. “Non-linear programming via penalty functions”. Management Sci.. 13 (1967), pp. 344–358.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer Science+Business Media New York
About this chapter
Cite this chapter
Di Pillo, G., Facchinei, F. (1989). Exact Penalty Functions for Nondifferentiable Programming Problems. In: Clarke, F.H., Dem’yanov, V.F., Giannessi, F. (eds) Nonsmooth Optimization and Related Topics. Ettore Majorana International Science Series, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6019-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6019-4_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-6021-7
Online ISBN: 978-1-4757-6019-4
eBook Packages: Springer Book Archive