An approximate dual subgradient algorithm for multi-agent non-convex optimization

Minghui Zhu, Sonia Martínez

    Research output: Contribution to journalArticlepeer-review

    83 Scopus citations


    We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective, constraint functions, and state constraint sets are convex. In order to deal with time-varying network topologies satisfying a standard connectivity assumption, we resort to consensus algorithm techniques and the Lagrangian duality method. We slightly relax the requirement of exact consensus, and propose a distributed approximate dual subgradient algorithm to enable agents to asymptotically converge to a pair of primal-dual solutions to an approximate problem. To guarantee convergence, we assume that the Slater's condition is satisfied and the optimal solution set of the dual limit is singleton. We implement our algorithm over a source localization problem and compare the performance with existing algorithms.

    Original languageEnglish (US)
    Article number6355622
    Pages (from-to)1534-1539
    Number of pages6
    JournalIEEE Transactions on Automatic Control
    Issue number6
    StatePublished - 2013

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering
    • Computer Science Applications
    • Electrical and Electronic Engineering


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