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تسجيل مستخدم جديدExponential Stability of Partial Primal-Dual Gradient Dynamics with Nonsmooth Objective Functions
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In this paper, we investigate the continuous time partial primal-dual gradient dynamics (P-PDGD) for solving convex optimization problems with the form $ minlimits_{xin X,yinOmega} f({x})+h(y), textit{s.t.} A{x}+By=C $, where $ f({x}) $ is strongly convex and smooth, but $ h(y) $ is strongly convex and non-smooth. Affine equality and set constraints are included. We prove the exponential stability of P-PDGD, and bounds on decaying rates are provided. Moreover, it is also shown that the decaying rates can be regulated by setting the stepsize.
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