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Since, then the Euler-Lagrange equation (22) of minimizing can be rewritten equivalently as (23).

Taking into account these constraints, the cost function to be minimized can be rewritten as follows: (7).

Furthermore, different objective functions to minimize can be pursued, for example, energy consumption, thermal discomfort, lifecycle costs, and polluting emissions.

This produces a separation of the objects into groups from which the metric to be minimized can be calculated.

Optimum genetic gains while minimizing inbreeding can be achieved by adopting appropriate selection and mating designs.

Using the steps outlined in Appendix B, the optimal and to minimize (23) can be obtained as (24).

The parameters are estimated such that an overall measure of errors is minimized, which can be accomplished using a nonlinear optimization procedure.

Accordingly, treatment-by-covariate interactions to explain heterogeneity or minimize inconsistency can be of a multidimensional nature as well.

A methodological imperative to minimize bias can be in conflict with the ethical principle of informed consent.

As a consequence, minimizing network losses can be transformed to minimizing load factor or load variance.

According to Lagrangian formalism, the optimal prices which minimizes (11) can be determined until the projected subgradient algorithm converges.