Sentence examples for higher order conditions from inspiring English sources

Later, Hagstrom and Hariharan (HH) suggested a method which used auxiliary functions and enabled implementation of higher order conditions.

Given that the first-order conditions are identically 0, their suggestion is to study the restrictions that the null imposes on higher order conditions.

More precisely, the Lie derivative is used to define the order of the state constraints, the Lie and Poisson brackets are used to analyze the singular extremals and to derive higher order optimality conditions, and the optimality conditions (order one, two and higher) are used to analyze the chattering extremals (see Section 3.4 for the chattering phenomenon).

Strong local epistatic interactions characterized by adaptive co-evolution, shape higher order global conditions and ultimately societal outcomes.

In some cases, the first-order conditions do not provide adequate information of the optimal control, and the higher order optimality conditions are needed.

The use of Poisson (and Lie) brackets simplifies the formulation of the higher order optimality conditions.

Also, higher order boundary conditions for stress tensor and heat flux are presented and discussed.

In this section we recall briefly the order of singular controls and the higher order optimality conditions.

It is worth noting that when the singular control is of order 1 (also called minimal order in [16, 34]), these higher order optimality conditions are not required.

The higher order boundary conditions imposed on the plastic flow have a large impact on the predicted strengthening.

The governing equations for nanobeam bending with the relevant higher order boundary conditions are then consistently derived.