Duality and Lower Bounds for Relative Projection Constants

Duality and Lower Bounds for Relative Projection Constants

On Maximal Relative Projection Constants

This article focuses on the maximum of relative projection constants over all m-dimensional subspaces of the N -dimensional coordinate space equipped with the max-norm. This quantity, called maximal relative projection constant, is studied in parallel with a lower bound, dubbed quasimaximal relative projection constant. Exploiting elegant expressions for these quantities, we show how they can b...

Online Lower Bounds via Duality

In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique for obtaining online deterministic and randomized lower bounds (i.e., hardness results) on the competitive ratio for a wide variety of problems. We show the ...

Monotone projection lower bounds from extended formulation lower bounds

In this short note, we show that the Hamilton Cycle polynomial, ∑ n-cycles σ ∏n i=1 xi,σ(i) is not a monotone sub-exponential-size projection of the permanent; this both rules out a natural attempt at a monotone lower bound on the Boolean permanent, and shows that the permanent is not complete for non-negative polynomials in VNPR under monotone p-projections. We also show that the cut polynomia...

Some Lower Bounds for Estrada Index