Related papers: Inf-sup stability implies quasi-orthogonality
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We establish quantitative stability results for classical distortion minimization problems in the theory of quasiconformal mappings. We consider the mean distortion functional and prove sharp stability estimates for the minimization…
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We consider the problem of designing uniformly stable first-order optimization algorithms for empirical risk minimization. Uniform stability is often used to obtain generalization error bounds for optimization algorithms, and we are…
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We improve the global Nekhoroshev stability for analytic quasi-convex nearly integrable Hamiltonian systems. The new stability result is optimal, as it matches the fastest speed of Arnold diffusion.
Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…
We analyze the two-field formulation of the quasi-static Biot's equations in bounded domains by means of the inf-sup theory. For this purpose, we exploit an equivalent four-field formulation of the equations, introducing the so-called total…
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Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…