<ul data-eligibleForWebStory="true"><li>Researchers propose a hierarchy of semidefinite relaxations for polynomial optimization problems (POP) on the nonnegative orthant.</li><li>POP on a semialgebraic set in the nonnegative orthant can be converted to an equivalent form by squaring each variable, allowing for easier computations.</li><li>The proposed hierarchy is based on extending Pólya's Positivstellensatz by Dickinson-Povh, introducing even symmetry and factor width concepts.</li><li>A key feature of the new hierarchy is the ability to choose the maximal matrix size of each semidefinite relaxation arbitrarily.</li><li>The sequence of values obtained by the hierarchy converges to the optimal value of the original POP at a rate of O(ε^(-c)), provided the semialgebraic set has a nonempty interior.</li><li>The method is applied to tasks such as robustness certification of multi-layer neural networks and computation of positive maximal singular values.</li><li>Compared to the Moment-SOS hierarchy, the proposed method offers better bounds and significantly faster computation times, running several hundred times faster.</li></ul>

Tractable hierarchies of convex relaxations for polynomial optimization on the nonnegative orthant

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