Tootfinder

Likelihood-informed Model Reduction for Bayesian Inference of Static Structural Loads
Jakob Scheffels, Elizabeth Qian, Iason Papaioannou, Elisabeth Ullmann
https://arxiv.org/abs/2510.07950

Likelihood-informed Model Reduction for Bayesian Inference of Static Structural Loads
Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian inverse problems is often expensive because standard solution approaches require many evaluations of the forward model mapping the parameter value to predicted observations. In many settings, this forward model is expensive because it requires the solution o…

Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum
Reza Rahimi Baghbadorani, Sergio Grammatico, Peyman Mohajerin Esfahani
https://arxiv.org/abs/2511.10239 https://arxiv.org/pdf/2511.10239 https://arxiv.org/html/2511.10239
arXiv:2511.10239v1 Announce Type: new
Abstract: We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function is the sum of two nonsmooth functions. With regard to convergence rate, we provide the global (optimal) sublinear convergence guarantees of O(1/k), which is known to be provably optimal for the studied class of functions, along with a local linear rate if the nonsmooth term fulfills a so-call locally strong convexity condition. We validate the performance of our algorithm on several problem classes, including regression with the l1-norm (the Lasso problem), sparse semidefinite programming (the MaxCut problem), Nuclear norm minimization with application in model free fault diagnosis, and l_1-regularized model predictive control to showcase the benefits of the coupling. An interesting observation is that although our global convergence result guarantees O(1/k) convergence, we consistently observe a practical transient convergence rate of O(1/k^2), followed by asymptotic linear convergence as anticipated by the theoretical result. This two-phase behavior can also be explained in view of the proposed smoothing rule.
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Verification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
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