monomial

Convex envelopes of bounded monomials on two-variable cones

  • Pietro Belotti
    • Categories Global Optimization Theory Tags , ,

    \(\) We consider an \(n\)-variate monomial function that is restricted both in value by lower and upper bounds and in domain by two homogeneous linear inequalities. Such functions are building blocks of several problems found in practical applications, and that fall under the class of Mixed Integer Nonlinear Optimization. We show that the upper envelope … Read more

    Error bounds for monomial convexification in polynomial optimization

  • Warren Adams
  • Akshay Gupte
  • Yibo Xu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , , , ,

    Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of $[0,1]^n$. This … Read more