An accelerated dual method based on analytical extrapolation for distributed quadratic optimization of largescale production complexes Abstract   Chemical production sites usually consist of plants that are owned by different companies or business units but are tightly connected by streams of materials and carriers of energy. Distributed optimization, where each entity optimizes its objective and the transfer prices of energy and materials are adapted by a coordinator, is a promising approach to this kind of problems, as confidentiality of internal data can be preserved. In this contribution, we propose an extension of the widely used subgradient methods for inequality constrained distributed QPs, which we call analytical extrapolation (AE). Therein, the analytical structure of the dual function is exploited to speed up convergence. Two strategies for handling changing sets of active constraints are presented. We investigate the performance of our algorithm on test problems, where different problem parameters are varied, and show that the performance of our algorithm is in most cases significantly better than that of other methods.

A unitary distributed subgradient method for multiagent optimization with different coupling sources Abstract   Distributed optimization techniques offer high quality solutions to various engineering problems, such as resource allocation and distributed estimation and control. In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed subgradient method with double averaging (abbreviated as      DSA    2     ) that only requires peertopeer communication and local computation to solve the global problem. The algorithmic framework builds on dual methods and dynamic average consensus; the sequence of test points is formed by iteratively minimizing a local dual model of the overall objective where the coefficients, i.e., approximated subgradients of the objective, are supplied by the dynamic average consensus scheme. We theoretically show that      DSA    2      enjoys nonergodic convergence properties, i.e., the local minimizing sequence itself is convergent, a distinct feature that cannot be found in existing results. Specifically, we establish a convergence rate of     O   (    1      t      )      in terms of objective function error. Then, extensions are made to tackle distributed optimization problems with coupled functional constraints by combining      DSA    2      and dual decomposition. This is made possible by Lagrangian relaxation that transforms the coupling in constraints of the primal problem into that in cost functions of the dual, thus allowing us to solve the dual problem via      DSA    2     . Both the dual objective error and the quadratic penalty for the coupled constraint are proved to converge at a rate of     O   (    1      t      )     , and the primal objective error asymptotically vanishes. Numerical experiments and comparisons are conducted to illustrate the advantage of the proposed algorithms and validate our theoretical findings.