Accession Number : AD0723803
Title : An Arc Method for Nonlinearly Constrained Programming Problems.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : McCormick,Garth P.
Report Date : JUN 1970
Pagination or Media Count : 38
Abstract : An algorithm using second derivatives for solving the problem: minimize f(x) subject to (g sub i) (x) = or > 0, i = 1, ..., m where the (g sub i) are not necessarily linear is presented. The basic idea is to generate a sequence of feasible points with decreasing objective function values by movement along piecewise smooth, 'almost' quadratic arcs. Cluster points of the sequence are shown to be second-order Kuhn-Tucker-Points. If the strict second order sufficiency conditions hold the rate of convergence is shown to be superlinear, or even quadratic if an additional Lipschitz condition is placed on the second derivatives of the problem functions. (Author)
Descriptors : (*NONLINEAR PROGRAMMING, ALGORITHMS), OPTIMIZATION, CONVERGENCE, ITERATIONS, THEOREMS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE