Keskeiset käsitteet
Efficient computation of minimizers for geometric programming problems.
Tiivistelmä
The content discusses the complexity of geometric programming in the Turing model and its application to nonnegative tensors. It covers coerciveness conditions, minimal points, iteration complexity bounds, and poly-time computation methods. The results provide insights into approximating spectral radii and maximum values efficiently.
Introduction:
Multidimensional arrays with d ⩾ 3 indices are prevalent in various fields.
Notation and preliminary results:
Cone of homogeneous polynomials with nonnegative coefficients.
Homogeneous polynomial maps.
Minimization of max of log-Laplace transforms.
Coerciveness condition:
Conditions for compact sublevel sets.
Minimal points:
Hessian interpretation and properties of minimizers.
A bound on Kmin(f) for coercive f:
Lower estimate of ν(A) based on set properties.
Poly-time computation of fmin:
Theorem on efficient computation with given precision ε.
Tilastot
Under a coercive assumption, an ε-minimizer can be computed in poly-time.
The spectral radius can be approximated within ε error in poly-time.