Convex Optimization · Problem 10.5

Interior-point methods — Boyd & Vandenberghe

Mathematics — Optimization · adding-quadratic-term-objective

Problem

Adding a quadratic term to the objective. Suppose Q⪰0Q \succeq 0. The problem minimizef(x)+(Ax−b)TQ(Ax−b)subject toAx=b\begin{array}{ll} \text{minimize} & f(x) + (Ax - b)^T Q(Ax - b) \\ \text{subject to} & Ax = b \end{array} is equivalent to the original equality constrained optimization problem (10.1). Is the Newton step for this problem the same as the Newton step for the original problem?

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