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• W1665831211 abstract "We study the asymptotic behavior of the solutions of evolution equations of the form $dot u(t)in -partial f(u(t),r(t))$, where $f(cdot ,r)$ is a one-parameter family of approximations of a convex function $f(cdot )$ we wish to minimize. We investigate sufficient conditions on the parametrization $r(t)$ ensuring that the integral curves $u(t)$ converge when $trightarrow infty$ towards a particular minimizer $u_infty$ of $f$. The speed of convergence is also investigated, and a result concerning the continuity of the limit point $u_infty$ with respect to the parametrization $r(cdot )$ is established. The results are illustrated on different approximation methods. In particular, we present a detailed application to the logarithmic barrier in linear programming." @default.
• W1665831211 created "2016-06-24" @default.
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• W1665831211 date "1999-08-30" @default.
• W1665831211 modified "2023-09-27" @default.
• W1665831211 title "Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence" @default.
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• W1665831211 doi "https://doi.org/10.1090/s0002-9947-99-02508-8" @default.
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