Exposing Constraints
研究了线性约束优化算法在无退化或线性独立假设下的识别性质，证明投影梯度收敛到零当且仅当迭代点进入并停留在负梯度暴露的面上。
The development of algorithms and software for the solution of large-scale optimization problems has been the main motivation behind the research on the identification properties of optimization algorithms. The aim of an identification result for a linearly constrained problem is to show that if the sequence generated by an optimization algorithm converges to a stationary point, then there is a nontrivial face F of the feasible set such that after a finite number of iterations, the iterates enter and remain in the face F. This paper develops the identification properties of linearly constrained optimization algorithms without any nondegeneracy or linear independence assumptions. The main result shows that the projected gradient converges to zero if and only if the iterates enter and remain in the face exposed by the negative gradient. This result generalizes results of Burke and Moré obtained for nondegenerate cases.