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A nonconvex optimization problem arising from distributed computing. (English) Zbl 1097.90565
Summary: We investigate the role of equity (fairness) in the Deadlock problem in a Distributed network, through the hierarchization of functioning rules by a stochastic model. The conclusion of the study highlights the role of equity in comparison with that of other (asymmetrical) functioning rules. In a first stage, we show that, in some directions, equity is an optimal functioning rule. We also prove in this stage that here exist other (asymmetrical) functioning rules equivalent to it, and we give their closed form expression. In a second stage, a deeper investigation of this question leads to optimizing a DC function (function representable as difference of two convex functions) of the form $$\sum_{k=1}^N\varphi(x_k)$$ over a simplex $$S=\{\overset \rightarrow x\in (]0,d^\prime[)^N| \sum^N_{k=1}x_k=d\}$$, where $$\frac {d}{N}<d^\prime<\operatorname {min}(1,d)$$ and $$d>0$$.

##### MSC:
 90C26 Nonconvex programming, global optimization
##### Keywords:
nonconvex optimization