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A new technique for nonconvex primal-dual decomposition of a large-scale separable optimization problem. (English) Zbl 0553.90087
The primal-dual approach is quite effective in decomposing a convex separable optimization problem into several subproblems of smaller sizes. In this paper, we present a new technique which extends the primal-dual approach to nonconvex problems. Since a straightforward application of the multiplier method destroys separability, a new Lagrangian function is proposed which preserves separability. Based on this new function we develop a new iterative method for finding an optimal solution to the problem and show that the method is locally convergent to an optimal solution. Furthermore, the effect of certain parameters on the ratio of convergence is investigated and simple examples are given to illustrate the proposed approach.

90C30Nonlinear programming
90C52Methods of reduced gradient type
65K05Mathematical programming (numerical methods)
49M37Methods of nonlinear programming type in calculus of variations
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