5. Saddlepoint Optimality Criteria of Nonlinear Programming without Differentiability
Society for Industrial and Applied Mathematics eBooks · 1994
Previous chapter Next chapter Classics in Applied Mathematics Nonlinear Programming5. Saddlepoint Optimality Criteria of Nonlinear Programming without Differentiabilitypp.69 - 82Chapter DOI:https://doi.org/10.1137/1.9781611971255.ch5PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutExcerpt The purpose of this chapter is to derive optimality criteria of the saddlepoint type for nonlinear programming problems. This type of optimality criterion is perhaps best illustrated by a simple example. Consider the problem of minimizing the function θ on the set X={x | x ∈ R,−x+2≦0} , where θ (x) = (x)2 . Obviously the solution is x ¯ =2 , and the minimum is θ ( x ¯ ) =4 . Previous chapter Next chapter RelatedDetails Published:1994ISBN:978-0-89871-341-1eISBN:978-1-61197-125-5 https://doi.org/10.1137/1.9781611971255Book Series Name:Classics in Applied MathematicsBook Code:CL10Book Pages:xvii + 219Key words:duality, equality constraints, concave functions, convex functions, Kuhn-Tucker, optimality