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We prove that the algorithm also works in those cases.
We prove that the algorithm achieves constant message and linear time complexity.
We will theoretically prove that the algorithm converges for a relevantly chosen initialization value.
We prove that the algorithm based on the smoothed penalty functions is convergent under mild conditions.
We prove that the algorithm always succeeds in constructing a Lyapunov function if the system possesses an exponentially stable equilibrium.
We propose a new family of valid cuts and prove that the algorithm is guaranteed to converge to optimality.
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In this paper, we investigate and analyze the nonconvex variational inequalities introduced by Noor in (Optim. Lett. 3 411-418, 2009) and (Comput. Math. Model. 21 97-108, 2010) and prove that the algorithms and results in the above mentioned papers are not valid.
Numerical results prove that proposed algorithm notably improves the overall throughput, while user fairness is guaranteed.
Meanwhile, in [8], the authors Combettes and Wajs also proved that the algorithm converged weakly.
They proved that the algorithm (1.14) converges weakly to some element of A-10.
It is proven that the algorithm converges to a Nash Equilibrium under certain conditions.
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