Hassan L. Hijazi

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

    An Outer-Inner Approximation for separable MINLPs

  • Pierre Bonami
  • Hassan L. Hijazi
  • Adam Ouorou
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software and Modeling Systems Tags , ,

    A common structure in convex mixed-integer nonlinear programs is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region. These … Read more

    An Outer-Inner Approximation for separable MINLPs

  • Pierre Bonami
  • Hassan L. Hijazi
  • Adam Ouorou
    • Categories (Mixed) Integer Nonlinear Programming Tags ,

    A common structure in convex mixed-integer nonlinear programs is additively separable nonlinear functions consisting of a sum of univariate functions. In the presence of such structures, we propose three improvements to the classical Outer Approximation algorithms that exploit separability. The first improvement is a simple extended formulation. The second a refined outer approximation. Finally, the … Read more

    Mixed Integer NonLinear Programs featuring “On/Off ” constraints: convex analysis and applications

  • Pierre Bonami
  • Gérard Cornuéjols
  • Hassan L. Hijazi
  • Adam Ouorou
    • Categories (Mixed) Integer Nonlinear Programming

    We call ”on/off” constraint an algebraic constraint that is activated if and only if a corresponding boolean variable is turned ”on” or equal to 1. Our main subject of interest is to derive tight convex formulations of Mixed Integer NonLinear Programs (MINLPs) featuring ”on/off” constraints. We study the simple set defined by one ”on/off” constraint … Read more