Exemplar Different-Level Quadratic Minimization, Division-by-Zero Issue, and Comparative Solutions

Different-level quadratic minimization (DLQM) is a novel-form optimization, hidden in diverse fields but not easy to be perceived. In this work, the basis solution of exemplar DLQM is proposed and investigated. First of all, through derivation of objective function with respect to high-level variable, the basis solution is obtained in a division expression, of which the denominator may be zero. Therefore, division-by-zero (DBZ) is attempted to be solved in this work. Three different methods [i.e., switching technique, Tikhonov regularization, and gradient dynamics (GD)] are applied to solving DBZ. Furthermore, numerical experiments of remedy solutions based on the methods are conducted.