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An exact penalty function for semi-infinite programming.(English)Zbl 0623.90069

The authors describe an exact penalty function for nonlinear semi- infinite programming. This function is a generalization of the \(\ell_ 1\) exact penalty function for nonlinear programming and may be used as a merit function for semi-infinite programming methods. The convex case as well as the nonconvex case (using some quadratic approximations) are considered. Moreover, an integral-inequality and asymptotic formula for certain functions have been proved; these results may be of more general interest.
Reviewer: R.Nehse

MSC:

90C30 Nonlinear programming
90C34 Semi-infinite programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
49M30 Other numerical methods in calculus of variations (MSC2010)
90C25 Convex programming

Cite

References:

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[2]D.P. Bertsekas,Constrained Optimization and Lagrange Multiplier Methods (Academic Press, New York, 1982). ·Zbl 0572.90067
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[11]H. Gfrerer, J. Guddat, Hj Wacker and W. Zulehner, ”Globalization of locally convergent algorithms for nonlinear optimization problems with constraints,” in: A.V. Fiacco and K.O. Kortanek, eds., Lecture notes in economic and mathematical system 215 (Springer-Verlag, New York, 1983) pp. 128–137. ·Zbl 0515.65050
[12]P.E. Gill, W. Murray and M.H. Wright,Practical Optimization (Academic Press, New York, 1981). ·Zbl 0503.90062
[13]S.-A. Gustafson, ”A three-phase algorithm for semi-infinite programs”, in: A.V. Fiacco and K.O. Kortanek, eds.,Semi-Infinite Programming and Applications, Lecture, notes in economics and mathematical systems 215 (Springer-Verlag, New York, 1983) pp. 138–157.
[14]R. Hettich, ed.,Semi-infinite Programming, Lecture notes in control and information sciences 15 (Springer-Verlag, New York, 1979). ·Zbl 0406.90063
[15]R. Hettich and W. Van Honstede, ”On quadratically convergent methods for semi-infinite programming,” in: R. Hettich, ed.,Semi-infinite Programming, Lecture notes in control and information science 15 (Springer-Verlag, New York, 1979) pp. 97–111. ·Zbl 0407.90074
[16]T. Pietrzykowski, ”An exact potential method for constrained maxima,”SIAM Journal of Numerical Analysis 6 (1969) 299–304. ·Zbl 0181.46501 ·doi:10.1137/0706028
[17]T. Pietrzykowski, ”The potential method for conditional maxima in locally compact metric spaces,”Numerische Mathematik 14 (1970) 325–329. ·Zbl 0195.46304 ·doi:10.1007/BF02165588
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[20]G.A. Watson, ”Numerical experiments with globally convergent methods for semi-infinite programming problems,” in: A.V. Fiacco and K.O. Kortanek, eds.,Semi-infinite Programming and Applications, Lecture notes in economics and mathematical systems 215 (Springer-Verlag, New York, 1983) pp. 193–205. ·Zbl 0513.65040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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