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Suppose that the constraint (7a) is satisfied with strict inequality, we can always multiply Q 0 by a scalar ν (ν<1) to make (7a) active, yet without decreasing the objective value of (7) and violating the total power constraint (7b).
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Finally, since solving for x0 in terms of the variables x4 and x5 (which are currently at zero value) yields x0 = 15 − x4 − x5, it can be seen that any further change in these slack variables will decrease the objective value.
The algorithm is shown to always decrease the objective function and to converge in a finite number of iterations.
Briefly, this table shows that the p-robust model decreases standard deviation in comparison with the robust model; similarly, it decreases the objective function of the proposed model.
Moreover, various cases are investigated to determine how to decrease the objective function (cost, mass flowrate, etc).
This may depend on the fact that the ADM-based optimization can decrease the objective function rapidly, as mentioned in many references [18 20].
Also, in theory, this study has proved that the proximal iteratively reweighted algorithm decreases the objective function value monotonically, and any limit point is a stationary point.
Finally, it has been proved that the algorithm can decrease the objective function value monotonically and any limit point is a stationary point.
For each (mathcal {C}_{i}), there will exist a vertex (v^{prime }_{i}) whose removal maximally decreases the objective function value.
The results show that with increasing the exergy unit cost, the optimum values of design parameters are selected such that to decrease the objective function.
In fact, by accepting any swap that decreases the objective function, we guarantee that the algorithm will eventually converge; even if the algorithm itself does not know when it happens.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com