Abstract
AbstractWe establish existence of steepest descent curves emanating from almost every point of a regular locally Lipschitz quasiconvex functions, where regularity means that the sweeping process flow induced by the sublevel sets is reversible. We then use max-convolution to regularize general quasiconvex functions and obtain a result of the same nature in a more general setting.
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. Lectures in Mathematics ETH Zürich;L. Ambrosio,2008
2. Attouch, H., Wets, R.: Quantitative stability of variational systems. II. A framework for nonlinear conditioning. SIAM J. Optim. 3(2), 359–381 (1993)
3. MOS-SIAM Series on Optimization;H. Attouch,2014
4. Aussel, D.: New developments in quasiconvex optimization. In: Fixed Point Theory, Variational Analysis, and Optimization, pp. 171–205. CRC Press, Boca Raton (2014)
5. Azé, D., Corvellec, J.-N.: Characterizations of error bounds for lower semicontinuous functions on metric spaces. ESAIM Control Optim. Calc. Var. 10(3), 409–425 (2004)