Performance spaces contain information about all combinations of attainable performance parameters of analog integrated circuits. Their exploration allows designers to evaluate given circuits without considering implementation details, making them a valuable tool to support the design process. The computation of performance spaces-even for a small number of considered parameters-is time-consuming because it requires solving multi-objective, non-convex optimization problems that involve costly circuit simulations. We present a numerical method for efficiently approximating high-dimensional performance spaces, which is based on the box-coverage method known from Pareto optimization. The resulting implementation not only outperforms state-of-the-art solvers based on the well-known Normal-Boundary Intersection method in terms of computational complexity, but also offers several advantages, such as a practical stopping criterion and the possibility of warm starting. Furthermore, we present an interactive visualization technique to explore performance spaces of any dimension, which can help system designers to make reliable topology decisions even without detailed technical knowledge of the underlying circuits. Numerical experiments that confirm the efficiency of our approach are performed by computing seven-dimensional performance spaces for an analog low-dropout regulator as used in the radio-frequency identification domain.

This paper presents an adaptation of the well-known normal boundary intersection (NBI) method for approximating complete feasible performance spaces of analog integrated circuits. Those spaces provide accurate information about all feasible combinations of competing performance parameters in a circuit. While the NBI-method is originally designed for computing the so-called Pareto front of a multi-objective optimization problem only, it can be adapted for approximating the complete performance space with some modifications. A scalarization into single-objective optimization problems is performed within our developed tool, which can be connected to any Spice-based simulator. Besides presenting the algorithm and its adaptations, the focus lies on investigating parallelization techniques and their effect on decreasing the computational time. Numerical experiments show the computed approximations of two- and three-dimensional performance spaces of several OTAs and compare the efficiencies of different parallelization schemes.

In this paper, a suitable measurement setup is presented and applied to conduct force and pressure measurements for transient contact cases with the shoulder at the example of lathe machine tending. Empirical measurements were executed on a selected collaborative robot's behavior regarding allowable operating speeds under consideration of sensor sensitivity, robot collision geometry, and damping materials. Comparisons between the theoretic calculations proposed in ISO/TS 15066 and the practical measurement results present a basis for future research. With the created database, preliminary risk assessment and economic assessment procedures of collaborative machine tending cells can be facilitated.

Regularized loss minimization, where a statistical model is obtained from minimizing the sum of a loss function and weighted regularization terms, is still in widespread use in machine learning. The statistical performance of the resulting models depends on the choice of weights (regularization parameters) that are typically tuned by cross-validation. For finding the best regularization parameters, the regularized minimization problem needs to be solved for the whole parameter domain. A practically more feasible approach is covering the parameter domain with approximate solutions of the loss minimization problem for some prescribed approximation accuracy. The problem of computing such a covering is known as the approximate solution gamut problem. Existing algorithms for the solution gamut problem suffer from several problems. For instance, they require a grid on the parameter domain whose spacing is difficult to determine in practice, and they are not generic in the sense that they rely on problem specific plug-in functions. Here, we show that a well-known algorithm from vector optimization, namely the Benson algorithm, can be used directly for computing approximate solution gamuts while avoiding the problems of existing algorithms. Experiments for the Elastic Net on real world data sets demonstrate the effectiveness of Benson’s algorithm for regularization parameter tracking.

Latent variable graphical models are an extension of Gaussian graphical models that decompose the precision matrix into a sparse and a low-rank component. These models can be learned with theoretical guarantees from data via a semidefinite program. This program features two regularization terms, one for promoting sparsity and one for promoting a low rank. In practice, however, it is not straightforward to learn a good model since the model highly depends on the regularization parameters that control the relative weight of the loss function and the two regularization terms. Selecting good regularization parameters can be modeled as a bi-level optimization problem, where the upper level optimizes some form of generalization error and the lower level provides a description of the solution gamut. The solution gamut is the set of feasible solutions for all possible values of the regularization parameters. In practice, it is often not feasible to describe the solution gamut efficiently. Hence, algorithmic schemes for approximating solution gamuts have been devised. One such scheme is Benson's generic vector optimization algorithm that comes with approximation guarantees. So far Benson's algorithm has not been used in conjunction with semidefinite programs like the latent variable graphical Lasso. Here, we develop an adaptive variant of Benson's algorithm for the semidefinite case and show that it keeps the known approximation and run time guarantees. Furthermore, Benson's algorithm turns out to be practically more efficient for the latent variable graphical model than the existing solution gamut approximation scheme on a wide range of data sets.