Current methods for computing vortex sheet separation use a regularization parameter which is discontinuous from the body to the vortex sheet. We propose two methods for reducing the errors associated with the discontinuity and improving convergence with respect to the regularization parameter. The ‘‘velocity smoothing” method is the simpler of the two, and removes the discontinuity in regulari...

In the solution of ill-posed problems by means of regularization methods, a crucial issue is the computation of the regularization parameter. In this work, we focus on the Truncated Singular Value Decomposition (TSVD) and Tikhonov method, and we define a method for computing the regularization parameter based on the behavior of Fourier coefficients. We compute a safe index for truncating the TS...

Solving discrete ill-posed problems via Tikhonov regularization introduces the problem of determining a regularization parameter. There are several methods available for choosing such a parameter, yet, in general, the uniqueness of this choice is an open question. Two empirical methods for determining a regularization parameter (which appear in the biomedical engineering literature) are the com...

We propose a Bayesian framework for learning the optimal regularization parameter in the L1-norm penalized least-mean-square (LMS) problem, also known as LASSO [1] or basis pursuit [2]. The setting of the regularization parameter is critical for deriving a correct solution. In most existing methods, the scalar regularization parameter is often determined in a heuristic manner; in contrast, our ...

Hyperparameter selection generally relies on running multiple full training trials, with hyperparameter selection based on validation set performance. We propose a gradient-based approach for locally adjusting hyperparameters during training of the model. Hyperparameters are adjusted so as to make the model parameter gradients, and hence updates, more advantageous for the validation cost. We ex...

This paper1 advances results in model selection by relaxing the task of optimally tuning the regularization parameter in a number of algorithms with respect to the classical cross-validation performance criterion as a convex optimization problem. The proposed strategy differs from the scope of e.g. generalized cross-validation (GCV) as it concerns the efficient optimization, not the individual ...

We consider two regularization approaches, the LASSO and the threshold-gradient-directed regularization, for estimation and variable selection in the accelerated failure time model with multiple covariates based on Stute's weighted least squares method. The Stute estimator uses Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective fun...