Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems - Archive ouverte HAL
Journal Articles Journal of Global Optimization Year : 2019

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

Michel Minoux
  • Function : Author
Riadh Zorgati

Abstract

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.
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Dates and versions

hal-03973917 , version 1 (05-02-2023)

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Michel Minoux, Riadh Zorgati. Sharp upper and lower bounds for maximum likelihood solutions to random Gaussian bilateral inequality systems. Journal of Global Optimization, 2019, 75 (3), pp.735-766. ⟨10.1007/s10898-019-00756-3⟩. ⟨hal-03973917⟩
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