4 papers · 1 filter
Variational convexity: new characterizations, calculus rules, and applications
Radu Ioan Bot, Ziyuan Wang
Introduced by R.T. Rockafellar in 2019, variational convexity is a generalized notion of convexity under which stationary points of nonconvex optimization problems can still be gua…
Level proximal subdifferential, variational convexity, and pointwise quadratic approximation
Honglin Luo, Xianfu Wang, Ziyuan Wang +1
Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level prox…
Every proximal mapping is a resolvent of level proximal subdifferential
Xianfu Wang, Ziyuan Wang
We propose a level proximal subdifferential for a proper lower semicontinuous function. Level proximal subdifferential is a uniform refinement of the well-known proximal subdiffere…
Calculus rules of the generalized concave Kurdyka-Łojasiewicz property
Xianfu Wang, Ziyuan Wang
In this paper, we propose several calculus rules for the generalized concave Kurdyka-Łojasiewicz (KL) property, which generalize Li and Pong's results for KL exponents. The optimal…