This manuscript proposes a geometric-programming (GP)-aided approach for reducing the conversion time of digitizers for resistive sensors. The digitizer, comprising a relaxation oscillator circuit, partitions the sensor span into multiple regimes. An optimization problem with the objective of minimizing the maximum conversion time for the multiple regimes, while maintaining lower limits to ON and OFF durations, is formulated. This constrained optimization problem is shown to be a GP and solved numerically. Optimal thresholds for partitioning the span as well as the optimal circuit parameters have been derived from the GP-based solution. It has been shown that the usage of GP, in the digitizer, can reduce the conversion time by at least a factor of three. The performance of the digitizer, designed with GP solutions, has been evaluated in simulation and experimental studies. Results show that the digital interface circuit requires only around 17 ms during the measurement range of 1 $\text{k}\Omega$ –1 $\text{M}\Omega$ and provides a nonlinearity of 0.2%.