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Article Dans Une Revue SIAM Journal on Optimization Année : 2019

In SDP relaxations, inaccurate solvers do robust optimization

Résumé

We interpret some wrong results (due to numerical inaccuracies) already observed when solving SDP-relaxations for polynomial optimization on a double precision floating point SDP solver. It turns out that this behavior can be explained and justified satisfactorily by a relatively simple paradigm. In such a situation, the SDP solver (and not the user) performs some `robust optimization' without being told to do so. Instead of solving the original optimization problem with nominal criterion $f$, it uses a new criterion $\tilde{f}$ which belongs to a ball $\mathbf{B}_\infty(f,\varepsilon)$ of small radius $\varepsilon>0$, centered at the nominal criterion $f$ in the parameter space. In other words the resulting procedure can be viewed as a `$\max-\min$' robust optimization problem with two players (the solver which maximizes on $\mathbf{B}_\infty(f,\varepsilon)$ and the user who minimizes over the original decision variables). A mathematical rationale behind this `autonomous' behavior is described.

Dates et versions

hal-01915976 , version 1 (08-11-2018)

Identifiants

Citer

Jean-Bernard Lasserre, Victor Magron. In SDP relaxations, inaccurate solvers do robust optimization. SIAM Journal on Optimization, 2019, 29 (3), pp.2128-2145. ⟨10.1137/18M1225677⟩. ⟨hal-01915976⟩
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