Optimality conditions in convex multiobjective SIP

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P

Postprandial effect of dietary fat quantity and quality on arterial stiffness and wave reflection:a randomised controlled trial

BACKGROUND: Arterial stiffness is a component of vascular function and an established risk factor for cardiovascular disease. There is a lack of conclusive evidence on the effect of a meal rich in monounsaturated fat (MUFA) compared with an isoenergetic meal rich in saturated fat (SFA) on postprandial vascular function and specifically on arterial stiffness. METHODS: Twenty healthy, non-smoking males (BMI 24 ± 2 kg/m(2); age 37.7 ± 14.4 y) participated in this single-blind, randomised, cross-over dietary intervention study. Each subject was randomised to receive a high-fat test-meal (3 MJ; 56 ± 2 g fat) at breakfast on 2 separate occasions, one rich in oleic acid (MUFA-meal) and one rich in palmitic acid (SFA-meal), and the meals were isoenergetic. Blood pressure (BP), arterial stiffness (PWV) and arterial wave reflection (augmentation index, AIx) were measured using applanation tonometry at baseline and every 30 minutes up to 4 hours after the ingestion of the test-meals. RESULTS: All subjects completed both arms of the dietary intervention. There was no significant difference in BP parameters, PWV or AIx at baseline between the two treatments (P > 0.05). There was a significant increase in brachial and aortic BP, mean arterial pressure (MAP), heart rate and PVW (time, P < 0.05) over the four hours after consumption of the fat-rich test-meal although the increase in PWV was no longer significant when adjusted for the increase in MAP. There was no difference in PWV between the two treatments (treatment*time, P > 0.05). There was a significant reduction in AIx (time, P < 0.05) over the four hour postprandial period although this was no longer significant when adjusted for the increase in heart rate and MAP (time, P > 0.05). There was no difference in AIx between the two treatments (treatment*time, P > 0.05). However, the reduction in heart rate corrected augmentation index (AIx(75)) was significant when corrected for the increase in MAP (time, P < 0.01) with no differential effect of the treatments (treatment*time, P > 0.05). CONCLUSIONS: This study has demonstrated a BP dependent increase in PWV and a decrease in arterial wave reflection in the four hour period in response to a high-fat meal. There was no evidence however that replacement of some of the SFA with MUFA had a differential effect on these parameters. The study highlights the need for further research to understand the effects of the substitution of SFA with MUFA on non-serum, new and emerging risk factors for CVD such as arterial stiffness