Revisiting Norm Optimization for Multi-Objective Black-Box Problems: A Finite-Time Analysis

The complexity of Pareto fronts imposes a great challenge on the convergence analysis of multi-objective optimization methods. While most theoretical convergence studies have addressed finite-set and/or discrete problems, others have provided probabilistic guarantees, assumed a total order on the solutions, or studied their asymptotic behaviour. In this paper, we revisit the Tchebycheff weighted method in a hierarchical bandits setting and provide a finite-time bound on the Pareto-compliant additive $\epsilon$-indicator. To the best of our knowledge, this paper is one of few that establish a link between weighted sum methods and quality indicators in finite time.Comment: submitted to Journal of Global Optimization. This article's notation and terminology is based on arXiv:1612.0841

Consumption of Pomegranate Juice Attenuates Exercise-Induced Oxidative Stress, Blood Pressure and Urinary Cortisol/Cortisone Ratio in Human Adults

Oxidative stress is exacerbated in overweight and obese individuals after acute exercise compared with their non-obese counterparts. Antioxidant supplementation of the diet may be one intervention to reduce exercise-induced oxidative stress in this vulnerable population. The aim of this study was to investigate whether polyphenol-rich pomegranate juice attenuates post-exercise oxidative stress and contributors to oxidative stress (glucocorticoids) and blood pressure in healthy overweight subjects. Healthy male and female subjects participated in a randomized placebo controlled parallel pilot-study (mean BMI: 26.7 ± 6.6 kg/m2). Two groups of participants (n=12) received either 500 ml/day of pomegranate juice (containing 1685 mg GAE) or placebo (matched for total energy). Participants completed two standardized 30 min treadmill tests (50% Wmax) at baseline and after one week of the intervention. Exercise-induced lipid peroxidation (MDA) was significantly lower following pomegranate juice consumption compared with placebo (31.2 ± 10.6 to 26.5 ± 9.8 MDA μmole/day) (p=0.035). Urinary free cortisol was reduced from 179.4 ± 53.2 to 125.6 ± 43.5 nmole/24h which was significant (p=0.042). In addition, there was an increase in urinary free cortisone from 112.2 ± 40.4 to 187.6 ± 90.2 nmole/24 h (p=0.045), and a significant decrease in the urinary free cortisol/cortisone ratio (p=0.009) from 1.6 ± 1.1 to 0.67 ± 0.55 following one week of pomegranate juice intake. Pomegranate juice consumption was also found to decrease systolic blood pressure pre-exercise (136.7 ± 11.7 to 131.8 ± 8.8 mmHg (p=0.007), and post-exercise from 158.8 ± 15.8 to 148.1 ± 12.3 mmHg (p<0.01) and diastolic blood pressure (86.3 ± 10.6 to 82.5 ± 6.8 mmHg (p=0.04) and 103.1 ± 12.5 to 93.9 ± 11.5 mmHg (p=0.001), pre and post exercise, respectively. Correlation between the change in cortisol/cortisone ratio with the effect on blood pressure showed a negative significant association post pomegranate juice intake (p=0.028 for systolic and p=0.008 for diastolic BP). There were no changes in lipid peroxidation or blood pressure following placebo treatment. In conclusion, these findings suggest that pomegranate juice consumption prior to an acute bout of moderate intensity exercise may help to alleviate exercise-induced oxidative stress, and lower blood pressure in the overweight and obese population