Quadratically constrained quadratic problems and cone optimization

Abstract

In this paper the problem of quadratic objective functions and quadratic constraints is presented, along with its transformation into a cone optimization problem. When transforming a nonlinear optimization problem by approximating nonlinear functions by using the quadratic and linear functions, new problems appear. The first is a quadratically constrained quadratic optimization problem with quadratic constraints (and optionally, linear), which may in turn be transformed into a cone optimization problem. In all three cases, these problems can be solved using internal point algorithms.