Solving indefinite quadratic programs by dynamical systems: Preliminary investigations

Preliminary results of our investigations on solving indefinite quadratic programs by dynamical systems are given.First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic programs are considered.Second, the existence and the uniqueness of the global solution of the dynamical system are proved by using some theorems from nonsmooth analysis and the theory of ordinary differential equations.Third, the strong pseudomonotonicity of the restriction of an affine operator on a closed convex set is analyzed in a special case.Finally, for a parametric indefinite quadratic program related to that special case, convergence of the trajectories of the dynamical system to the Karush-Kuhn-Tucker points is established.The elementary direct proofs in the third and fourth topics would be useful for understanding the meaning and significance of several open problems proposed in this paper.