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WBD recommends shareholders reject Paramount's unsolicited cash bid, calling the offer "illusory" and saying it believes Netflix's proposal is still superior (Wall Street Journal)
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Churchill reminds us: "Success is not final, failure is not fatal." Resilience is the key! Every setback is an invitation for a comeback. How do you keep your drive alive in challenging times? Let’s use each obstacle as a Stepping Stone to Success! 🚀
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On fundamental properties of high-order forward-backward envelope
Alireza Kabgani, Masoud Ahookhosh
https://arxiv.org/abs/2511.10421 https://arxiv.org/pdf/2511.10421 https://arxiv.org/html/2511.10421
arXiv:2511.10421v1 Announce Type: new
Abstract: This paper studies the fundamental properties of the high-order forward-backward splitting mapping (HiFBS) and its associated forward-backward envelope (HiFBE) through the lens of high-order regularization for nonconvex composite functions. Specifically, we (i) establish the boundedness and uniform boundedness of HiFBS, along with the H\"older and Lipschitz continuity of HiFBE; (ii) derive an explicit form for the subdifferentials of HiFBE; and (iii) investigate necessary and sufficient conditions for the differentiability and weak smoothness of HiFBE under suitable assumptions. By leveraging the prox-regularity of $g$ and the concept of $p$-calmness, we further demonstrate the local single-valuedness and continuity of HiFBS, which in turn guarantee the differentiability of HiFBE in neighborhoods of calm points. This paves the way for the development of gradient-based algorithms tailored to nonconvex composite optimization problems.
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