On global minimization for general p-regularized subproblems with p>2 (Nonlinear Analysis and Convex Analysis)

Abstract

The p-regularized subproblem (p-RS) is a regularizing term for computing a Newton-like step for unconstrained optimization, which incorporates a weighted regularization term displaystyle frac{$sigma$}{p}Vert xVert^{p}. In this article, we resolve the global minimizers of (mathrm{p}-RS) for p>2 with necessary and sufficient optimality conditions.