A general technique for dealing with degeneracy in reduced gradient methods for linearly constrained nonlinear programming
For the nonlinear programming problem `\(f(x)\to\min\)', \(x\in\mathbb{R}\), where \(R= \{x\in \mathbb{R}^ n/Ax= b, x\geq 0\}\) a general model of reduced gradient algorithms is presented. For the given algorithms, non- degeneracy assumptions are not required. Under the assumption of continuous differentiability of the objective function \(f(x)\), the authors prove that either the sequence \(\{x^ k\}\) generated by the algorithm terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of this sequence is a Kuhn-Tucker point.
scientific article; zbMATH DE number 597374
scientific article