This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semi-definite programming relaxations. Three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.
H. L. Hijazi and C. Coffrin and P. Van Hentenryck "Convex Quadratic Relaxations of Mixed-Integer Nonlinear Programs in Power Systems" Mathematical Programming Computation 2016