Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Micronutrient Deficits Are Still Public Health Issues among Women and Young Children in Vietnam

Background: The 2000 Vietnamese National Nutrition Survey showed that the population’s dietary intake had improved since 1987. However, inequalities were found in food consumption between socioeconomic groups. As no national data exist on the prevalence of micronutrient deficiencies, a survey was conducted in 2010 to assess the micronutrient status of randomly selected 1526 women of reproductive age and 586 children aged 6–75 mo. Principal Findings: In women, according to international thresholds, prevalence of zinc deficiency (ZnD, 67.262.6%) and vitamin B12 deficiency (11.761.7%) represented public health problems, whereas prevalence of anemia (11.661.0%) and iron deficiency (ID, 13.761.1%) were considered low, and folate (,3%) and vitamin A (VAD,,2%) deficiencies were considered negligible. However, many women had marginal folate (25.1%) and vitamin A status (13.6%). Moreover, overweight (BMI$23 kg/m 2 for Asian population) or underweight occurred in 20 % of women respectively highlighting the double burden of malnutrition. In children, a similar pattern was observed for ZnD (51.963.5%), anemia (9.161.4%) and ID (12.961.5%) whereas prevalence of marginal vitamin A status was also high (47.362.2%). There was a significant effect of age on anemia and ID prevalence, with the youngest age group (6–17 mo) having the highest risk for anemia, ID, ZnD and marginal vitamin A status as compared to other groups. Moreover, the poorest groups of population had a higher risk for zinc, anemia and ID

Constrained Extremum Problems, Regularity Conditions and Image Space Analysis. Part II: The Vector Finite-Dimensional Case

The scalar \ufb01nite-dimensional case has been discussed in the \ufb01rst part of this work series, which aims at exploiting the image space analysis to establish a general regularity condition for constrained extremum problems. Based on this preliminary result, the present paper dedicates itself to further study the regularity conditions for vector constrained extremum problems in a Euclidean space. The case of in\ufb01nite-dimensional image will be the subject of a subsequent paper