Naohiko Arima

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

    A Quadratically Constrained Quadratic Optimization Model for Completely Positive Cone Programming

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

    We propose a class of quadratic optimization problems whose exact optimal objective values can be computed by their completely positive cone programming relaxations. The objective function can be any quadratic form. The constraints of each problem are described in terms of quadratic forms with no linear terms, and all constraints are homogeneous equalities, except one … Read more