Let $mathcal{G}$ be a compact group and let $f_{ij} in L^2(mathcal{G})$.We define the Non-Unique Games (NUG) problem as finding $g_1,dots,g_n inmathcal{G}$ to minimize $sum_{i,j=1}^n f_{ij} left( g_i g_j^{-1}ight)$. Wedevise a relaxation of the NUG problem to a semidefinite program (SDP) bytaking the Fourier transform of $f_{ij}$ over $mathcal{G}$, which can then besolved efficiently. The NUG framework can be seen as a generalization of thelittle Grothendieck problem over the orthogonal group and the Unique Gamesproblem and includes many practically relevant problems, such as the maximumlikelihood estimator} to registering bandlimited functions over the unit spherein $d$-dimensions and orientation estimation in cryo-Electron Microscopy.
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机译：让$ mathcal {g} $是一个紧凑的组，让$ f_ {ij} in l ^ 2（ mathcal {g}）$。我们将非唯一游戏（nug）问题定义为查找$ g_1，点，g_n in mathcal {g} $最小化$ sum_ {i，j = 1} ^ n f_ {ij} left（g_i g_j ^ { - 1} oled）$。窗口放松一个SEMIDEFINITE程序（SDP）迷住$ f_ {ij} $ over $ mathcal {g} $的傅立叶变换，然后可以有效地膨胀。核磁框架可以看作是在正交组和独特的GamesProck上的Thelittle Grochendieck问题的概括，并且包括许多实际相关的问题，例如Maximumlikelihial估计器}，以通过单位Spherein $ D $ D $ D $ -dimensions和方向估计来注册带状函数在冷冻电子显微镜下。
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