»ã±¨±êÌâ (Title)£ºGeneralized Nash Equilibrium Problems£¨¹ãÒåÄÉʲƽºâÎÊÌ⣩

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»ã±¨ÌáÒª£º We study generalized Nash equilibrium problems (GNEPs) that are given by polynomial or rational functions. Lagrange multiplier expressions and feasible extensions are introduced to compute generalized Nash equilibria (GNEs). We give a hierarchy of polynomial optimization relaxations to solve the GNEP. The Moment-SOS relaxations are applied to solve the rational optimization problems. Under some genericity assumptions, we show that the proposed hierarchy can compute a GNE if it exists or detect its nonexistence. Numerical experiments are given to show the efficiency of the proposed method.