Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Estimation of the nadir objective vector is an important task, particularly for multi-objective optimization problems having more than two conflicting objectives. Along with the ideal point, nadir point can be used to normalize the objectives so that multi-objective optimization algorithms can be used more reliably. The knowledge of the nadir point is also a pre-requisite to many multiple crite...

A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can b...

It is proposed to use two points of support when estimating the nadir vector components in Multiobjective Linear Programming (MOLP) problems: to consider the frontier of the feasible set S and to use the reference point method. The proposed approach gives upper bounds of the estimated values.

Background: stereotactic body radiotherapy (SBRT) has emerged as an effective treatment for localized prostate cancer. However, prostate-specific antigen (PSA) kinetics after SBRT has not been well characterized. The objective of the current study is to analyze the rate of PSA decline and PSA nadir following hypofractonated SBRT in localized prostate cancer. Materials and Methods: From 2008...

according adhar bigdili, muhammad ali was son of abdal biq naqqashbashi (painter laureate)and grandson of aliquli biq jabadar, court painter of shah safi and shah abbas ii safawi. adhar bigdili credited muhammad ali with naqqashbashi of shah tahmasp ii safawi and nadir shah afshar. having learnt the art of painting from his father, muhamma ali in turn trained ali ashraf, who worked under patron...

Nadir objective vector is constructed with the worst Pareto-optimal objective values in a multi-objective optimization problem and is an important entity to compute because of its importance in estimating the range of objective values in the Pareto-optimal front and also in using many interactive multi-objective optimization techniques. It is needed, for example, for normalizing purposes. The t...

(1) An important point is the large bias (30-50%) between OMI (KNMI DOMINO v2.0) and SCIAMACHY nadir (KNMI-BIRA TM4NO2A v2.3) retrievals, especially if both data sets are photochemically converted. It is puzzling me because Dirksen et al. (2011) and Hendrick et al. (2012) found a good agreement between OMI, SCIAMACHY nadir and groundbased observations, suggesting the absence of such a large bia...