Month: December 2003

Convergence rate estimates for the gradient differential inclusion

  • Osman Guler
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    Let f be a lower semi-continuous convex function in a Euclidean space, finite or infinite dimensional. The gradient differential inclusion is a generalized differential equation which requires that -x'(t) be in the subgradient of f at x. It is the continuous versions of the gradient descent method for minimizing f in case f is differentiable, … Read more

    Generating functions and duality for integer programs

  • Jean-Bernard Lasserre
    • Categories Global Optimization Theory, Integer Programming

    We consider the integer program P -> max {c’x | Ax=y; x\in N^n }. Using the generating function of an associated counting problem, and a generalized residue formula of Brion and Vergne, we explicitly relate P with its continuous linear programming (LP) analogue and provide a characterization of its optimal value. In particular, dual variables … Read more