作者：He, Chang; Jiang, Yuntian; Zhang, Chuwen; Ge, Dongdong; Jiang, Bo; Ye, Yinyu
作者单位：Shanghai University of Finance & Economics; Shanghai Jiao Tong University; Stanford University
摘要：This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric eigenvalue procedures and thus grant an advantage in ill-conditioned problems. Moreover, GHM extends the ordinary homogeneous model (Zhang et al. A homogenous second-order descent method for nonconvex optimization, 2022. arXiv:2211.08212 [math]) to allow ada...
作者：Leyffer, Sven; Manns, Paul
作者单位：United States Department of Energy (DOE); Argonne National Laboratory; Dortmund University of Technology
摘要：McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state cons...
