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VI-constrained hemivariational inequalities: distributed algorithms and power control in ad-hoc networks

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Abstract

We consider centralized and distributed algorithms for the numerical solution of a hemivariational inequality (HVI) where the feasible set is given by the intersection of a closed convex set with the solution set of a lower-level monotone variational inequality (VI). The algorithms consist of a main loop wherein a sequence of one-level, strongly monotone HVIs are solved that involve the penalization of the non-VI constraint and a combination of proximal and Tikhonov regularization to handle the lower-level VI constraints. Minimization problems, possibly with nonconvex objective functions, over implicitly defined VI constraints are discussed in detail. The methods developed in the paper are then used to successfully solve a new power control problem in ad-hoc networks.

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Notes

  1. Here and in all the paper, when we say that a function is continuous or continuously differentiable on a closed set, we intend that the function is (defined and) continuous or continuously differentiable on an open set containing the closed set.

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Authors and Affiliations

  1. Department of Computer, Control and Management Engineering Antonio Ruberti, University of Rome La Sapienza, Via Ariosto 25, 00185 , Rome, Italy

    Francisco Facchinei & Lorenzo Lampariello

  2. Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, IL, USA

    Jong-Shi Pang

  3. Department of Electrical Engineering State University of New York (SUNY) at Buffalo, Buffalo, NY, USA

    Gesualdo Scutari

Authors
  1. Francisco Facchinei
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  2. Jong-Shi Pang
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  3. Gesualdo Scutari
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  4. Lorenzo Lampariello
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Correspondence to Francisco Facchinei.

Additional information

The work of the first author has been partially supported by MIUR-PRIN 2005 n.2005017083 Research Program “Innovative Problems and Methods in Nonlinear Optimization”. The work of the second author was based on research partially supported by the U.S.A. National Science Foundation grant CMMI 0969600 and by the Air Force Office of Sponsored Research award No. FA9550-09-10329.

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Facchinei, F., Pang, JS., Scutari, G. et al. VI-constrained hemivariational inequalities: distributed algorithms and power control in ad-hoc networks. Math. Program. 145, 59–96 (2014). https://doi.org/10.1007/s10107-013-0640-5

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  • DOI: https://doi.org/10.1007/s10107-013-0640-5

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