An Arc Method for Nonlinearly Constrained Programming Problems.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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An algorithm using second derivatives for solving the problem minimize fx 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
- Operations Research