Summary
This paper contains the mathematical validation of a new approach to mathematical programming problems based on a penalty function method. The given problem is replaced by a second „auxiliary“ problem which, in many cases may be solved by standard methods since it involves the maximization of a concave function of a single variable over an interval. The auxiliary problem is defined implicitly in therms of the constituents of the original problem. Examples are presented in order to illustrate the theoretical results.
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Falk, J.E. A relaxed interior approach to nonlinear programming. Z. Wahrscheinlichkeitstheorie verw Gebiete 11, 327–337 (1969). https://doi.org/10.1007/BF00531654
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DOI: https://doi.org/10.1007/BF00531654