nonconvex quadratic optimization

A Gentle, Geometric Introduction to Copositive Optimization

  • Samuel Burer
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    This paper illustrates the fundamental connection between nonconvex quadratic optimization and copositive optimization—a connection that allows the reformulation of nonconvex quadratic problems as convex ones in a unified way. We intend the paper for readers new to the area, and hence the exposition is largely self-contained. We focus on examples having just a few variables … Read more

    Simplified Copositive and Lagrangian Relaxations for Linearly Constrained Quadratic Optimization Problems in Continuous and Binary Variables

  • Naohiko Arima
  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    For a quadratic optimization problem (QOP) with linear equality constraints in continuous nonnegative variables and binary variables, we propose three relaxations in simplified forms with a parameter $\lambda$: Lagrangian, completely positive, and copositive relaxations. These relaxations are obtained by reducing the QOP to an equivalent QOP with a single quadratic equality constraint in nonnegative variables, … Read more