In this paper, two novel approaches to unmanned underwater vehicle path planning are presented. The main idea of the first approach, referred to as Constrained Optimization (CO) is to represent the free space of the workspace as a set of inequality constraints using vehicle configuration variables. The second approach converts robot path planning into a Semi-infinite Constrained Optimization (SCO) problem. The function interpolation technique is adopted to satisfy the start and goal configuration requirements. Mathematical foundations for Constructive Solid Geometry (CSG), Boolean operations and approximation techniques are also presented to reduce the number of constraints, and to avoid local minima. The advantages of these approaches are that the mature techniques developed in optimization theory which guarantee convergence, efficiency and numerical robustness can be directly applied to the robot path planning problem. Simulation results have been presented.