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        "event_title":"German Convo on the Go",
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        "description":"Meet at Burton Tower for a 1-hour walk and talk in German with Mary Gell (magell@umich.edu). This event happens 'rain or shine.' Open to speakers of German at all levels.",
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        "tags":["European","German","German Studies","Germanic Languages And Literatures","Humanities","Language"],
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        "datetime_start":"20261014T160000",
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        "event_title":"Kullback\u2013Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria",
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        "combined_title":"Kullback\u2013Leibler Mirror-Prox for Measure-Valued Variational Inequalities and Mean-Field Equilibria: Ziqing Zhang, UM",
        "event_subtitle":"Ziqing Zhang, UM",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"We study the computation of static mean-field equilibria on a compact state space by formu-\nlating the equilibrium condition as a variational inequality over probability measures. We propose\nan entropic variant of Korpelevich\u2019s extragradient algorithm\u2014the Kullback\u2013Leibler Mirror-Prox\nmethod\u2014in which Euclidean projections are replaced by relative-entropy proximal steps. Each\nhalf-step is therefore an explicit exponential reweighting of the current measure, implemented on a\nfinite state-space discretization. Under Lasry\u2013Lions monotonicity and continuity assumptions, we\nprove convergence of mesh-refined ergodic averages and obtain finite-iteration Minty-residual and\napproximate-equilibrium bounds that jointly quantify iteration and discretization errors. Under\nstrong monotonicity, we derive metric convergence rates for the last, best, and averaged iterates.\nWe also develop a KL-type Tikhonov regularization that selects the equilibrium minimizing relative\nentropy with respect to a reference measure. The framework applies to potential and nonpotential\ncost operators and does not require differentiability or convexity of the cost in the individual state.\n\nJoint work with Erhan Bayraktar, Ibrahim Ekren and Lu Vy.",
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