Previous article Next article An Existence Theorem for Penalty Function TheoryJ. P. Evans and F. J. GouldJ. P. Evans and F. J. Gouldhttps://doi.org/10.1137/0312039PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA necessary condition is presented for the existence of global maxima of penalty functions without a barrier. This condition with one additional restriction is proved to be sufficient.[1] C. M. Ablow and , Georges Brigham, An analog solution of programming problems, J. Operations Res. Soc. Amer., 3 (1955), 388–394 MR0073323 CrossrefISIGoogle Scholar[2] R. R. Allran and , S. E. J. Johnsen, An algorithm for solving nonlinear programming problems subject to nonlinear inequality constraints, Comput. J., 13 (1970), 171–177 10.1093/comjnl/13.2.171 MR0264833 0191.17104 CrossrefISIGoogle Scholar[3] G. D. Camp, Inequality constrained stationary value problems, Operations Research, 3 (1955), 548–550 CrossrefISIGoogle Scholar[4] J. P. Evans and , F. J. Gould, Stability and exponential penalty function techniques in nonlinear programming, Institute of Statistics Mimeo Series No. 723, Department of Statistics, University of North Carolina, Chapel Hill, 1970 Google Scholar[5] J. P. Evans, , F. J. Gould and , J. W. Tolle, Exact penalty functions in nonlinear programming, Math. Programming, 4 (1973), 72–97, Department of Statistics, University of North Carolina at Chapel Hill, 1972 10.1007/BF01584647 MR0319575 0267.90079 CrossrefGoogle Scholar[6] Anthony V. Fiacco and , Garth P. McCormick, Nonlinear programming: Sequential unconstrained minimization techniques, John Wiley and Sons, Inc., New York-London-Sydney, 1968xiv+210 MR0243831 0193.18805 Google Scholar[7] F. H. Murphy, A class of exponential penalty functions, Tech. Rep., Graduate School of Business, Rutgers University, Newark, N.J., 1971 Google Scholar[8] T. Pietrzykowski, Application of the steepest descent method to concave programming, Proc. IFIPS Congress (Munich), North-Holland, Amsterdam, 1962 Google Scholar[9] Willard I. Zangwill, Non-linear programming via penalty functions, Management Sci., 13 (1967), 344–358 MR0252040 0171.18202 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Unconstrained Convex Programming Approach to Linear Semi-Infinite ProgrammingSIAM Journal on Optimization, Vol. 8, No. 2 | 31 July 2006AbstractPDF (315 KB) Volume 12, Issue 3| 1974SIAM Journal on Control351-579 History Submitted:15 March 1973Published online:18 July 2006 InformationCopyright © 1974 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0312039Article page range:pp. 509-516ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics