This paper is an exploration of numerical optimization as it applies to the consumer choice problem. Suggested algorithms are intended to compute solutions to the Marshallian problem, and some can extend to the dual given the suggested modifications. Each method seeks to either weaken the sufficient conditions for optimization, converge to a solution more efficiently, or describe additional properties of the decision space. The purpose of this paper is to explore constrained quasiconvex programming in a less complicated environment by design of Marshallian constraints.

The main purpose of this project is to create a method for determining the absolute position of an accelerometer. Acceleration and angular speed were obtained from an accelerometer attached to a vehicle as it moves around. As the vehicle moves to collect information the orientation of the accelerometer changes, so a rotation matrix is applied to the data based on the angular change at each time. The angular change and distance are obtained by using the trapezoidal approximation of the integrals. This method was first validated by using simple sets of "true" data which are explicitly known sets of data to compare the results to. Then, an analysis of how different time steps and levels of noise affect the error of the results was performed to determine the optimal time step of 0.1 sec that was then used for the actual tests. The tests that were performed were: a stationary test for uses of calibration, a straight line test to verify a simple test, and a closed loop test to test the accuracy. The graphs for these tests give no indication of the actual paths, so the final results can only show that the data from the accelerometer is too noisy and inaccurate for this method to be used by this sensor. The future work would be to test different ways to get more accurate data and then use it to verify this methods. These ways could include using more sensors to interpolate the data, reducing noise by using a different sensor, or adding a filter. Then, if this method is considered accurate enough, it could be implemented into control systems.