An Arc Method for Nonlinearly Constrained Programming Problems.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1970
- Accession Number
- AD0723803
Entities
People
- Garth P. Mccormick
Organizations
- University of Wisconsin–Madison