Carleton Coffrin

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

  • Ksenia Bestuzheva
  • Carleton Coffrin
  • Hassan L. Hijazi
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Convex Optimization Tags , , , ,

    This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent … Read more

    Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Lifted Nonlinear Cuts

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , ,

    This paper considers state-of-the-art convex relaxations for the AC power flow equations and introduces new valid cuts based on convex envelopes and lifted nonlinear constraints. These valid linear inequalities strengthen existing semidefinite and quadratic programming relaxations and dominate existing cuts proposed in the litterature. Together with model intersections and bound tightening, the new linear cuts … Read more

    Polynomial SDP Cuts for Optimal Power Flow

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , , ,

    The use of convex relaxations has lately gained considerable interest in Power Systems. These relaxations play a major role in providing quality guarantees for non-convex optimization problems. For the Optimal Power Flow (OPF) prob- lem, the semidefinite programming (SDP) relaxation is known to produce tight lower bounds. Unfortunately, SDP solvers still suffer from a lack … Read more

    Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Basic Sciences Applications, Convex Optimization, Global Optimization Applications Tags , , , , ,

    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 … Read more