The main object of this paper is to prove that for a linear or convex multiobjective program, a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set. ᮊ

We have analyzed some parameters of porphyrin metabolism in 60 patients with end-stage renal failure, 20 of them on CAPD and the remaining on HD. In comparison with 56 control subjects, both groups of patients showed the three following findings: low erythrocyte aminolevulinate dehydrase activity, inhibition ability for the activity of this enzyme when their plasma was incubated in vitro with normal erythrocytes, and increased plasma porphyrin levels. Like anemia, these abnormalities were more remarkable in patients on HD who also exhibited increased erythrocyte protoporphyrin levels and compensatory porphobilinogen deaminase activities. Mean weekly porphyrin removal through dialysate was higher in CAPD (90.8 micrograms) than in HD patients (30.4 micrograms). Dialysate and plasma porphyrins were correlated in both circumstances (r = 0.714, P < 0.01 and r = 0.637, P < 0.05, respectively). The less pronounced porphyrin abnormalities found in CAPD patients with respect to HD patients may be due to the more efficient capability of peritoneal dialysis for removing from plasma protein-bound substances, as porphyrins and inhibitors of aminolevulinate dehydrase or other enzymes involved in erythropoiesis. Since no close relationship was found between these abnormalities of porphyrin metabolism and hematocrit values, the anemia of uremia cannot be merely considered as a direct consequence of altered heme biosynthetic pathway.

Several results are established concerning the density of the set of ideal points in the set of minimal solutions of positive support functionals of sets in normed linear spaces. The above ideal points are de®ned and several charac terizations and sucient conditions for their existence are also stated.

Duality theory is applied to measure the sensitivity of a multi-objective programming problem. Since the dual problem does not always measure primal sensitivity, the paper states necessary and sufficient conditions (homogeneity conditions) to guarantee the existence and uniqueness of a pair of solutions (primal and dual) such that the dual solution provides the primal sensitivity.

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