Appendices for " Finding Second-Order Stationary Points Efficiently in Smooth Nonconvex Linearly Constrained Optimization Problems " A Details of Implementation of Algorithms

In this section, we will elaborate more about the ideas of designing SNAP . First, we give the main motivation of selecting the update directions. Next, we will give the detailed algorithm description of the line search used in SNAP . A.2 Line Search Algorithm To understand the algorithm, let us first define the set of inactive constraints as A Lemma 2. If there exists an index i A (x Therefore, the line search algorithm reduces to the classic unconstrained update. If so, then the algorithm either touches the boundary without increasing the objective, or it has already achieved sufficient descent.