  Incorporating the auxiliary information into the survey estimation is a
fundamental problem in survey sampling. Calibration weighting is a popular tool
for incorporating the auxiliary information. The calibration weighting method
of Deville and Sarndal (1992) uses a distance measure between the design
weights and the final weights to solve the optimization problem with
calibration constraints. This paper introduces a novel framework that leverages
generalized entropy as the objective function for optimization, where design
weights play a role in the constraints to ensure design consistency, rather
than being part of the objective function. This innovative calibration
framework is particularly attractive due to its generality and its ability to
generate more efficient calibration weights compared to traditional methods
based on Deville and Sarndal (1992). Furthermore, we identify the optimal
choice of the generalized entropy function that achieves the minimum variance
across various choices of the generalized entropy function under the same
constraints. Asymptotic properties, such as design consistency and asymptotic
normality, are presented rigorously. The results from a limited simulation
study are also presented. We demonstrate a real-life application using
agricultural survey data collected from Kynetec, Inc.
