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

Michel Minoux () and Riadh Zorgati ()
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Michel Minoux: UPMC
Riadh Zorgati: EDF Lab Paris-Saclay R&D OSIRIS

Journal of Global Optimization, 2019, vol. 75, issue 3, No 6, 735-766

Abstract: 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.

Keywords: Random Gaussian inequalities; Joint probability maximization; Global optimization; Fenchel transform; Concave envelopes (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00756-3

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