We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange algorithm (REX). Numerical comparisons suggest that the performance of REX is comparable or superior to the performance of state-ofthe-art methods across a broad range of problem structures and sizes. We focus on the most commonly used criterion of D-optimality that also has applications beyond experimental design, such as the construction of the minimum volume ellipsoid containing a given set of data-points. For D-optimality, we prove that the proposed algorithm converges to the optimum. We also provide formulas for the optimal exchange of weights in the case of the criterion of A-optimality. These formulas enable one to use REX for computing A-optimal and I-optimal designs.

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AimTo assess the quality of self‐assessment and the attitude of healthcare workers (HCWs) to hand hygiene (HH) as possible factors of unsatisfactory HH compliance in clinical practice.BackgroundNoncompliance of HH causes healthcare‐acquired infections (HAI) in patients. It is assumed that HH‐related infections make up approximately 80% of all infections in clinical practice. Our observations suggest that self‐assessment and attitude might be surprisingly important factors.Design and methodThe cross‐sectional approach using questionnaire and direct observation was applied. We followed STROBE guidelines. In total, questionnaires of 639 HCWs of surgical departments were included in the study, and 127 HCWs had been also directly observed.ResultsHigh self‐assessment regarding HH compliance and its knowledge was reported by 74% and 83% of HCWs, respectively. At the same time, only 51% of HCWs positively evaluated their colleagues with respect to HH. Similar to previous studies, we have found significant differences between physicians and nurses regarding the level of self‐assessment, attitude and perception of HH. Physicians were more critical in self‐assessment and considered HH less important compared to nurses. The observations revealed drawbacks in HH practices. The high level of self‐overassessment might be a contributing factor to noncompliance with HH.ConclusionsIt is necessary to establish systematic professional training and education of HCWs in relation to their HH, and to continuously monitor and evaluate the level of self‐assessment in clinical practice, mainly in surgery.Relevance to clinical practiceA reasonable objective level of self‐assessment and attitude to HH are the most important conditions for preventing of HAI in patients.

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In the paper, we solve the problem of computing the maximin efficient design with respect to the class of all orthogonally invariant criteria. It turns out that on a finite experimental domain, the maximin efficient design can be computed by the methods of semidefinite programming. Using this approach, we can deal with the non-differentiability inherent in the problem, due to which the standard iterative procedures cannot be applied. We illustrate the results on the models of polynomial regression on a line segment and quadratic regression on a cube.