We study the cyclic steepest descent method (CSD) for strictly convex quadratic minimization. CSD repeats, for j consecutive iterations, the exact steepest-descent step size computed at the beginning of each cycle. The only rigorous result for the real algorithm has so far been restricted to two dimensions, where the c...
We study the semi-discrete quadratic Wasserstein energy. The energy is nonsmooth at collisions of sites. We prove local Lipschitz continuity on the full configuration space, together with global semiconcavity, coercivity, and dissipativity; show that every global minimizer is interior and collision free; and establish...
This paper proposes an inexact interior-point relaxation method (iIPRM) for LO problems that does not require its iterates to remain strictly positive and employs a sparse preconditioner tailored to the structure of the normal matrix.
Rui-Jin Zhang, Yu-Hong Dai, Xin-Wei Liu et al.· Journal of Optimization Theo...· 0 citations
The critical points and local minimizers of the model are characterized, a sufficient-condition result for rank recovery is provided, and whole-sequence convergence of the proposed algorithms under explicit step-size and inertial-parameter conditions are proved using the Kurdyka--\L{}ojasiewicz framework.
Yu-Ling He, Ran Gu· 0 citations
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