Finite convergence of algorithms for nonlinear programs and variational inequalities

Algorithms for nonlinear programming and variational inequality problems are, in general, only guaranteed to converge in the limit to a Karush-Kuhn-Tucker point, in the case of nonlinear programs, or to a solution in the case of variational inequalities. In this paper, we derive sufficient conditions for nonlinear programs with convex feasible sets such that any convergent algorithm can be modified, by adding a convex subproblem with a linear objective function, to guarantee finite convergence in a generalized sense. When the feasible set is polyhedral, the subproblem is a linear program and finite convergence is obtained. Similar results are also developed for variational inequalities.

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