A Predictor–Corrector Gaussian Homotopy (PCGH) method is proposed that formulates Gaussian homotopy optimization as a path tracking problem, and geometry-aware arc-length parameterizations based on Fisher-information and Hessian-derived metrics are introduced for efficient approximation of the Gaussian convolution and its derivatives.
PANDA is proposed, a matrix-free solver for differentiable NMPC that achieves much faster forward and backward computation and lower memory overhead than representative differentiable optimization solvers, while maintaining effective imitation learning performance.
Yuan-Kun Chen, Zi-Fei Nie, Xun Gong et al.· 1 citation
Nonlinear preconditioning makes it possible to adapt gradient updates to the growth of the objective's curvature, but combining its design with suitable stepsize selection is challenging. We propose adaptive dual preconditioned gradient descent (adaptive DPGD), which combines curvature-based preconditioner design with...
Modern real application problems involve matrix-valued parameters, yet conventional optimizers treat them as vectors, thereby motivating matrix-aware methods that exploit input-output geometry, such as Muon which orthogonalizes the momentum matrices before parameter updates. Its empirical success raises a conceptual qu...
The proposed reformulation of the total scaled-gradient variation regularizer achieves PSNR and SSIM competitive with or superior to representative variational methods, especially at high noise levels, and improves the structural reconstruction under dense and sparse scanning.
Hai-Bin Su, Chunlin Wu, Huibin Chang et al.· 0 citations
Differentiating through parametric optimization problems is central to bilevel programming and meta-learning, often accomplished using approximate implicit differentiation. The implicit function theorem requires inverting a partial Jacobian of the optimality condition, which fails when there are many solutions. Nonethe...
Baptiste Plaquevent-Jourdain, Jalal Fadili, Antonio Silveti-Falls· 0 citations
This article derives a projected gradient flow characterized by tangent and normal cone decompositions, which capture the local geometry of the constraint set and shows that constraint geometry continuously filters gradient directions along the optimization trajectory, leading to a trajectory-dependent implicit regular...
Yan-Jun Yan· Big Data· 0 citations
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