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We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level problems. In particular, we consider MIBLPs with upper-level constraints that involve lower-level variables. We assume that the inducible region is nonempty and all variables are bounded. By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm. The solution procedure is enhanced by a projection strategy that does not require the relatively complete response property. To ensure its performance, we prove that our new method converges to the global optimal solution in a finite number of iterations. A large-scale computational study on random instances and instances of hierarchical supply chain planning are presented to demonstrate the effectiveness of the algorithm.

The aim of this paper is to investigate the use of Spanish and Korean reformulation markers against the backdrop of a contrastive / intercultural rhetoric approach (Kaplan, 1966; Hinds, 1987; Clyne, 1994; Connor, 2008, 2011). In order to carry out the analysis, following a line of previous research papers in Murillo (2007, 2012), an empirical study using Spanish and Korean journalistic corpus was performed. The results obtained demonstrate significant disparity between the use of Spanish and Korean RMs when approached from a linguistic-intercultural rhetoric perspective, more specifically as to the use of double reformulation -the repetition of the Korean markers (jeuk… jeuk… / got… got…)-, some particular rhetorical patterns of the Korean marker got, denoting its cultural idiosyncrasy, and the discourse processes, such as ‘definition’, ‘denomination’, and ‘conclusion’, utilizing the selected markers in the two languages.

The Karush–Kuhn–Tucker and value function (lower-level value function, to be precise) reformulations are the most common single-level transformations of the bilevel optimization problem. So far, these reformulations have either been studied independently or as a joint optimization problem in an attempt to take advantage of the best properties from each model. To the best of our knowledge, these reformulations have not yet been compared in the existing literature. This paper is a first attempt towards establishing whether one of these reformulations is best at solving a given class of the optimistic bilevel optimization problem. We design a comparison framework, which seems fair, considering the theoretical properties of these reformulations. This work reveals that although none of the models seems to particularly dominate the other from the theoretical point of view, the value function reformulation seems to numerically outperform the Karush–Kuhn–Tucker reformulation on a Newton-type algorithm. The computational experiments here are mostly based on test problems from the Bilevel Optimization LIBrary (BOLIB).

To quantify total sugar reformulation in Canadian prepackaged foods and beverages between 2013 and 2017 and identify changes in the nutritional composition of the foods and beverages reformulated to be lower in total sugar. Longitudinal examination of foods and beverages present in both 2013 and 2017 collections of the University of Toronto's Food Label Information Program database (n 6628 matched products). The proportion of products with changes in sugar levels was determined. Wilcoxon signed-rank test was used to examine changes in sugar levels overall for products lower or higher in sugar and changes in nutrient composition for products lower in sugar. Largest grocery retailers by market share in Canada. Canadian prepackaged foods and beverages. The majority (76·6 %) of products had no change in total sugar content, 12·4 % were reformulated to be lower in sugar and 11·0 % were higher in sugar. A median sugar reduction of 19·0 % (1·6 g) was seen among products lower in sugar which was offset by a median 18·0 % (1·5 g) increase among products higher in sugar. Overall, median levels of energies and other nutrients stayed the same or decreased among products reformulated to be lower in sugar, the exception was for starch, which increased. Limited progress was made to reformulate foods and beverages to be lower in total sugar between 2013 and 2017. Results from this study identify areas in the food supply where attention may be needed to avoid unintended consequences of sugar-focused reformulation in terms of overall nutritional composition.

Background The consumption of free sugars in the UK is more than double the guideline intake for adults and close to triple for children, with soft drinks representing a significant proportion. The aim of this study was to assess how individual soft drink companies and consumers have responded to calls to reduce sugar consumption, including the soft drink industry levy (SDIL), between 2015 and 2018. Methods This was an annual cross-sectional study using nutrient composition data of 7377 products collected online, paired with volume sales data for 195 brands offered by 57 companies. The main outcome measures were sales volume, sugar content and volume of sugars sold by company and category, expressed in total and per capita per day terms. Results Between 2015 and 2018, the volume of sugars sold per capita per day from soft drinks declined by 30%, equivalent to a reduction of 4.6 g per capita per day. The sales-weighted mean sugar content of soft drinks fell from 4.4 g/100 ml in 2015 to 2.9 g/100 ml in 2018. The total volume sales of soft drinks that are subject to the SDIL (i.e. contain more than 5 g/100 ml of sugar) fell by 50%, while volume sales of low- and zero-sugar (< 5 g/100 ml) drinks rose by 40%. Conclusion Action by the soft drinks industry to reduce sugar in products and change their product portfolios, coupled with changes in consumer purchasing, has led to a significant reduction in the total volume and per capita sales of sugars sold in soft drinks in the UK. The rate of change accelerated between 2017 and 2018, which also implies that the implementation of the SDIL acted as an extra incentive for companies to reformulate above and beyond what was already being done as part of voluntary commitments to reformulation, or changes in sales driven by consumer preferences.

Portion sizes of many foods have increased over time. However, the size of effect that reducing food portion sizes has on daily energy intake and body weight is less clear. We used a systematic review methodology to identify eligible articles that used an experimental design to manipulate portion size served to human participants and measured energy intake for a minimum of 1 d. Searches were conducted in September 2020 and again in October 2021. Fourteen eligible studies contributing eighty-five effects were included in the primary meta-analysis. There was a moderate-to-large reduction in daily energy intake when comparing smaller v. larger portions (Standardised Mean Difference (SMD) = –0·709 (95 % CI: –0·956, –0·461), approximately 235 kcal (983·24 kJ)). Larger reductions to portion size resulted in larger decreases in daily energy intake. There was evidence of a curvilinear relationship between portion size and daily energy intake; reductions to daily energy intake were markedly smaller when reducing portion size from very large portions. In a subset of studies that measured body weight (four studies contributing five comparisons), being served smaller v. larger portions was associated with less weight gain (0·58 kg). Reducing food portion sizes may be an effective population-level strategy to prevent weight gain.

Despite the importance of the perception behind teachers' feedback, it is astonishing to note that there are not many studies regarding how teachers provide feedback. Drawing upon Ellis’ (2009) typology of written Corrective Feedback (CF), this study explored the most common feedback types provided by EFL teachers. Moreover, the study aimed at finding out whether teachers’ teaching experience and learners’ proficiency level had any bearing on the type of feedback the teachers provided. Eleven teachers provided feedback on 301 descriptive essays written by EFL students in English. The findings revealed that teachers mostly tended to employ direct CF to correct their students’ linguistic errors. This was followed by indirect CF and metalinguistic CF, respectively. It came to light that focused CF, electronic feedback, and reformulation had no popularity among Iranian EFL teachers. The experienced teachers opted more for indirect feedback while the inexperienced ones preferred direct feedback.  Teachers were more inclined to provide intermediate students with direct CF whereas they provided more indirect CF to the upper intermediate students. The results suggest that not all teachers’ perceptions about feedback can necessarily be rendered into classroom practices and various factors, including culture, society, learners and teachers themselves impact teachers’ beliefs and practices.

The nutritional reformulation of processed food and beverage products has been promoted as an important means of addressing the nutritional imbalances in contemporary dietary patterns. The focus of most reformulation policies is the reduction in quantities of nutrients-to-limit – Na, free sugars, SFA, trans-fatty acids and total energy. The present commentary examines the limitations of what we refer to as ‘nutrients-to-limit reformulation’ policies and practices, particularly when applied to ultra-processed foods and drink products. Beyond these nutrients-to-limit, there are a range of other potentially harmful processed and industrially produced ingredients used in the production of ultra-processed products that are not usually removed during reformulation. The sources of nutrients-to-limit in these products may be replaced with other highly processed ingredients and additives, rather than with whole or minimally processed foods. Reformulation policies may also legitimise current levels of consumption of ultra-processed products in high-income countries and increased levels of consumption in emerging markets in the global South.

Background Dietary energy density is thought to be a contributor to obesity, but the extent to which different magnitudes and types of reductions to food energy density decreases daily energy intake is unclear. The primary objective was to systematically review and meta-analyse experimental studies that have examined the effect that manipulating energy density of food has on total daily energy intake. Secondary objectives were to examine moderators of the effect that altering energy density has on daily energy intake and effects on body weight. Methods A systematic review and multi-level meta-analysis of studies on human participants that used an experimental design to manipulate the energy density of foods served and measured energy intake for a minimum of 1 day. Results Thirty-one eligible studies sampling both children ( n  = 4) and adults ( n  = 27) contributed 90 effects comparing the effect of higher vs. lower energy density of served food on daily energy intake to the primary meta-analysis. Lower energy density of food was associated with a large decrease in daily energy intake (SMD = − 1.002 [95% CI: − 0.745 to − 1.266]). Findings were consistent across studies that did vs. did not manipulate macronutrient content to vary energy density. The relation between decreasing energy density and daily energy intake tended to be strong and linear, whereby compensation for decreases to energy density of foods (i.e. by eating more at other meals) was minimal. Meta-analysis of ( n  = 5) studies indicated that serving lower energy dense food tended to be associated with greater weight loss than serving higher energy dense food, but this difference was not significant (− 0.7 kg difference in weight change, 95% CIs: − 1.34, 0.04). Conclusions Decreasing the energy density of food can substantially reduce daily energy intake and may therefore be an effective public health approach to reducing population level energy intake. Trial registration Registered on PROSPERO ( CRD42020223973 ).

We study linear programming relaxations of nonconvex quadratic programs given by the reformulation–linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible regions of a quadratic program and its RLT relaxation. We establish various connections between recession directions, boundedness, and vertices of the two feasible regions. Using these properties, we present a complete description of the set of instances that admit an exact RLT relaxation. We then give a thorough discussion of how our results can be converted into simple algorithmic procedures to construct instances of quadratic programs with exact, inexact, or unbounded RLT relaxations.