2,710 research outputs found
Randomized Constraints Consensus for Distributed Robust Mixed-Integer Programming
In this paper, we consider a network of processors aiming at cooperatively
solving mixed-integer convex programs subject to uncertainty. Each node only
knows a common cost function and its local uncertain constraint set. We propose
a randomized, distributed algorithm working under asynchronous, unreliable and
directed communication. The algorithm is based on a local computation and
communication paradigm. At each communication round, nodes perform two updates:
(i) a verification in which they check---in a randomized fashion---the robust
feasibility of a candidate optimal point, and (ii) an optimization step in
which they exchange their candidate basis (the minimal set of constraints
defining a solution) with neighbors and locally solve an optimization problem.
As main result, we show that processors can stop the algorithm after a finite
number of communication rounds (either because verification has been successful
for a sufficient number of rounds or because a given threshold has been
reached), so that candidate optimal solutions are consensual. The common
solution is proven to be---with high confidence---feasible and hence optimal
for the entire set of uncertainty except a subset having an arbitrary small
probability measure. We show the effectiveness of the proposed distributed
algorithm using two examples: a random, uncertain mixed-integer linear program
and a distributed localization in wireless sensor networks. The distributed
algorithm is implemented on a multi-core platform in which the nodes
communicate asynchronously.Comment: Submitted for publication. arXiv admin note: text overlap with
arXiv:1706.0048
Randomized constraints consensus for distributed robust mixed-integer programming
open4siThis work was supported in part
by the European Research Council (ERC) under the European Union’s
Horizon 2020 Research and Innovation Programme under Grant 638992
- OPT4SMART, and in part by a grant from the Singapore National
Research Foundation (NRF) under the ASPIRE Project under Grant
NCR-NCR001-040.In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable, and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: 1) A verification in which they check - in a randomized fashion - the robust feasibility of a candidate optimal point, and 2) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As a main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached) so that candidate optimal solutions are consensual. The common solution has proven to be - with high confidence - feasible and, hence, optimal for the entire set of uncertainty except a subset having an arbitrarily small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multicore platform in which the nodes communicate asynchronously.embargoed_20210317Chamanbaz M.; Notarstefano G.; Sasso F.; Bouffanais R.Chamanbaz M.; Notarstefano G.; Sasso F.; Bouffanais R
A scenario approach for non-convex control design
Randomized optimization is an established tool for control design with
modulated robustness. While for uncertain convex programs there exist
randomized approaches with efficient sampling, this is not the case for
non-convex problems. Approaches based on statistical learning theory are
applicable to non-convex problems, but they usually are conservative in terms
of performance and require high sample complexity to achieve the desired
probabilistic guarantees. In this paper, we derive a novel scenario approach
for a wide class of random non-convex programs, with a sample complexity
similar to that of uncertain convex programs and with probabilistic guarantees
that hold not only for the optimal solution of the scenario program, but for
all feasible solutions inside a set of a-priori chosen complexity. We also
address measure-theoretic issues for uncertain convex and non-convex programs.
Among the family of non-convex control- design problems that can be addressed
via randomization, we apply our scenario approach to randomized Model
Predictive Control for chance-constrained nonlinear control-affine systems.Comment: Submitted to IEEE Transactions on Automatic Contro
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