Two-level primal-dual decomposition technique for large-scale nonconvex optimization problems with constraints
The authors are concerned with the separable minimization problem \[ (1)\quad \text{ minimize } f(x)=\sum^{N}_{i=1}f_ i(x_ i)\text{ subject to } h(x)=\sum^{N}_{i=1}h_ i(x_ i)=0, \] \(g_ i(x_ i)\leq 0\) \((i=1,...,N)\), where \(x\in R^ n\), \(x_ i\in R^{n_ i}\), \(n=\sum^{N}_{i=1}n_ i\), \(f_ i:\) \(R^{n_ i}\to R\), \(h_ i:\) \(R^{n_ i}\to R^ m\), \(g_ i:\) \(R^{n_ i}\to R^{\ell_ i}\). To solve (1) by the dual method of decomposition in case of nonconvexity, several techniques have been proposed. Some of them are three-level primal-dual optimization structures or apply to (1) without the inequality constraint \(g_ i(x_ i)\leq 0\). In this paper the authors consider for solving (1) a technique introduced in a previous paper of the first author [Automatica 25, No.2, 233-242 (1989; Zbl 0685.49023)], give a convergence analysis and provide numerical results.
two-level primal-dual decomposition technique
scientific article; zbMATH DE number 4174670