Immunizing Conic Quadratic Optimization Problems Against Implementation Errors

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchi’s robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma

Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization

Learning Professional Knowledge: Bachelor Nursing Students’ Experiences in Learning and Knowledge Quality Outcomes in a Competence-Based Curriculum

Since decades, nursing education struggles with a persistent gap between the theoretical knowledge offered in the study program and its application in professional practice. To bridge this gap competence-based curricula were developed with instructional designs as authentic learning contexts and self-directed learning. In this project we explored final year Bachelor Nursing (BN) students’ experiences in learning in a newly developed curriculum, and their knowledge quality outcomes and the degree of agreement with knowledge requirements. An instrumental multiple case study was conducted with interviews, concept mapping and a domain knowledge list. Results show that a third of the participants had positive learning experiences and got high appraisals for their knowledge quality. Similar to the medium and low scoring participants, they developed instrumental knowledge but integrated other forms of learning into a system of meaning, which is needed to solve non-routine problems in future practice. Medium and low scoring participants did not profit from learning in authentic contexts and self-directed learning. In conclusion, developing sufficient professional knowledge in a constructivist competence-based curriculum is influenced by students’ intrinsic motivation to build a strong knowledge base, by their perception of how to learn and use professional knowledge, and their expectations of the degree of supervision and guidance by the teacher. It is recommended to evaluate the extent to which the intended curriculum is being taught

Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.

Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.robust optimization;ø-divergence;goodness-of-fit statistics

Developing the logic framework underpinning a whole-systems approach to childhood overweight and obesity prevention:Amsterdam Healthy Weight Approach

Abstract Background Whole‐systems approaches (WSAs) are well placed to tackle the complex local environmental influences on overweight and obesity, yet there are few examples of WSAs in practice. Amsterdam Healthy Weight Approach (AHWA) is a long‐term, municipality‐led program to improve children's physical activity, diet, and sleep through action in the home, neighborhood, school, and city. Adopting a WSA, local political, physical, social, educational, and healthcare drivers of childhood obesity are viewed as a complex adaptive system. Since 2013, AHWA has reached >15,000 children. During this time, the estimated prevalence of 2–18‐year‐olds with overweight or obesity in Amsterdam has declined from 21% in 2012 to 18.7% in 2017. Declining trends are rarely observed in cities. There is a need to formally articulate AHWA program theory in order to: (i) inform future program evaluation which can interpret this decline within the context of AHWA and (ii) contribute a real‐life example of a WSA to the literature. Methods This study aimed to formally document the program theory of AHWA to permit future evaluation. A logic framework was developed through extensive document review and discussion, during program implementation. Results The working principles of the WSA underpinning AHWA were made explicit in an overarching theory of change, articulated in a logic framework. The framework was operationalized using an illustrative example of sugar intake. Conclusions The logic framework will inform AHWA development, monitoring, and evaluation and responds to a wider need to outline the working principles of WSAs in public health

Long Range Order at Low Temperature in Dipolar Spin Ice

Recently it has been suggested that long range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to ${\rm Dy_{2}Ti_{2}O_{7}}$ and ${\rm Ho_{2}Ti_{2}O_{7}}$.Comment: New version of the manuscript. Now contains 3 POSTSCRIPT figures as opposed to 2 figures. Manuscript contains a more detailed discussion of the (i) nature of long-range ordered ground state, (ii) finite-size scaling results of the 1st order transition into the ground state. Order of authors has been changed. Resubmitted to Physical Review Letters Contact: [email protected]