ITERATIVE ALGORITHM FOR TRIPLE-HIERARCHICAL CONSTRAINED NONCONVEX OPTIMIZATION PROBLEM AND ITS APPLICATION TO NETWORK BANDWIDTH ALLOCATION.

In this paper, we discuss a variational inequality problem with the gradient of a nonconvex objective function in which the constraint set composed of the absolute set and the subsidiary sets is not feasible. We formulate a compromise solution of the problem by using a solution to a variational inequality for the gradient over a subset of the absolute set with the elements closest to the subsidiary sets in terms of the norm. The objective of this paper is to enable us to discuss a network bandwidth allocation problem with a nonconcave utility function in which the compoundable constraints about the preferable transmission rate fall in the infeasible region. For such a bandwidth allocation, the ideal bandwidth must be quickly shared among traffic sources so as to satisfy the capacity constraints (absolute constraints) and all sources' demands regarding the transmission rate (subsidiary constraints) as much as possible. Iterative algorithms for the bandwidth allocation should thus not involve auxiliary optimization problems or complicated computations. Here, we devise an algorithm based on an iterative technique for triple-hierarchical constrained nonconvex optimization to achieve the optimal bandwidth allocation. Numerical examples for the bandwidth allocation demonstrate the effectiveness and convergence of the proposed algorithm. [ABSTRACT FROM AUTHOR]