The maximum principle with lack of monotonicity

Monotonicity and the Pareto Principle

The property of monotonicity, th criterion of (first-degree) income dominance and the Pareto principle appear frequently in the literature on the axiomatic approach to the welfare economics of income distribution. Sometimes these are regarded as almost interchangeable for practical purposes. However, as we shall show, this interchangeability arises because of other important assumptions that ar...

Evaluating Matching Algorithms: the Monotonicity Principle

In this paper we present the monotonicity principle, a sufficient condition to ensure that exact mapping, a mapping as would be performed by a human observer, is ranked close to the best mapping, as generated automatically by a matching algorithm. The research is motivated by the introduction of the semantic Web vision and the shift towards machine understandable Web resources. We support the i...

The Pontryagin Maximum Principle

Theorem (PontryaginMaximum Principle). Suppose a final time T and controlstate pair (û, x̂) on [τ, T ] give the minimum in the problem above; assume that û is piecewise continuous. Then there exist a vector of Lagrange multipliers (λ0, λ) ∈ R × R with λ0 ≥ 0 and a piecewise smooth function p: [τ, T ] → R n such that the function ĥ(t) def =H(t, x̂(t), p(t), û(t)) is piecewise smooth, and one has ̇̂ ...

The Principle of Maximum Conformality

A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale of the running coupling αs(μ ). It is common practice to guess a physical scale μ = Q which is of order of a typical momentum transfer Q in the process, and then vary the scale over a range Q/2 and 2Q. This procedure is clearly problematic since the resulting fixed-order pQCD...

The Maximum Principle of Pontryagin