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Zbl 0553.90087
Tanikawa, Akio; Mukai, Hiro
A new technique for nonconvex primal-dual decomposition of a large-scale separable optimization problem. (English)
[J] IEEE Trans. Autom. Control 30, 133-143 (1985). ISSN 0018-9286

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.

MSC 2000:: *90C30 Nonlinear programming
90C52 Methods of reduced gradient type
65K05 Mathematical programming (numerical methods)
49M37 Methods of nonlinear programming type

Keywords: nonconvex primal-dual decomposition; large-scale separable optimization; separability preserving Lagrange function; primal-dual approach; optimal solution; convergence

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