Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems

  • Michel Minoux
  • Riadh ZorgatiEmail author


This paper focuses on finding a solution maximizing the joint probability of satisfaction of a given set of (independent) Gaussian bilateral inequalities. A specially structured reformulation of this nonconvex optimization problem is proposed, in which all nonconvexities are embedded in a set of 2-variable functions composing the objective. From this, it is shown how a polynomial-time solvable convex relaxation can be derived. Extensive computational experiments are also reported, and compared to previously existing results, showing that the approach typically yields feasible solutions and upper bounds within much sharper confidence intervals.


Random Gaussian inequalities Joint probability maximization Global optimization Fenchel transform Concave envelopes 



Three anonymous Reviewers are gratefully acknowledged for all remarks and constructive comments which resulted in an improved revised version of the paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LIP6UPMCParis Cedex 05France
  2. 2.EDF Lab Paris-Saclay R&D OSIRISPalaiseauFrance

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