GRADIENT FLOWS, SECOND-ORDER GRADIENT SYSTEMS AND CONVEXITY

Abstract : We disclose an interesting connection between the gradient flow of a e(2)-smooth function psi and strongly evanescent orbits of the second-order gradient system defined by the square-norm of del psi under an adequate convexity assumption. As a consequence, we obtain the following surprising result for two C-2, convex, and bounded from below functions psi(1), psi(2) if parallel to del psi(1)parallel to = parallel to del psi(2)parallel to, then psi(1) = psi(2) + k for some k is an element of R.
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Submitted on : Monday, July 1, 2019 - 11:36:34 AM
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Tahar Z. Boulmezaoud, Philippe Cieutat, Aris Daniilidis. GRADIENT FLOWS, SECOND-ORDER GRADIENT SYSTEMS AND CONVEXITY. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2018, 28 (3), pp.2049-2066. ⟨10.1137/16M1153418⟩. ⟨hal-02169449⟩

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