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This paper is focused on the convergence analysis of an adaptive stochastic collocation algorithm for the stationary diffusion equation with parametric coefficient. The algorithm employs sparse grid collocation in the parameter domain…
Orthogonal matching pursuit (OMP) is a greedy algorithm popularly being used for the recovery of sparse signals. In this paper, we study the performance of OMP for support recovery of sparse signal under noise. Our analysis shows that under…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
We introduce a planner designed to guide robot manipulators in stably placing objects within intricate scenes. Our proposed method reverses the traditional approach to object placement: our planner selects contact points first and then…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Time-bin encoded photon pairs enable robust, decoherence-resistant transmission through optical fibers for long-distance quantum communication, where phase noise poses a critical limitation to stable operation. Here, we implement an…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
This paper proposes a general framework for constructing feedback controllers that drive complex dynamical systems to "efficient" steady-state (or slowly varying) operating points. Efficiency is encoded using generalized equations which can…
The use of algorithmic predictions in decision-making leads to a feedback loop where the models we deploy actively influence the data distributions we see, and later use to retrain on. This dynamic was formalized by Perdomo et al. 2020 in…
Feedback optimization is an increasingly popular control paradigm to optimize dynamical systems, accounting for control objectives that concern the system operation at steady-state. Existing feedback optimization techniques heavily rely on…
Porting code from CPU to GPU is costly and time-consuming; Unless much time is invested in development and optimization, it is not obvious, a priori, how much speed-up is achievable or how much room is left for improvement. Knowing the…
We prove new optimality results for adaptive mesh refinement algorithms for non-symmetric, indefinite, and time-dependent problems by proposing a generalization of quasi-orthogonality which follows directly from the inf-sup stability of the…
Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes…
This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…
Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
In this paper we develop linear transfer Perron Frobenius operator-based approach for optimal stabilization of stochastic nonlinear system. One of the main highlight of the proposed transfer operator based approach is that both the theory…
We demonstrate that accurate computation of the spectral proper orthogonal decomposition (SPOD) critically depends on the choice of frequency resolution. Using both artificially generated data and large-eddy simulation data of a turbulent…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…