We have devised a method to generate non-overlapping random dot patterns for light guides and diffuser films in liquid crystal displays (LCDs). Molecular-dynamics-based algorithms are being for this purpose and have been proven to generate high quality dot patterns. The key technical challenge is how to remove inter-dot overlap that leads to visible roughness in the luminance distribution. In this paper, we describe a new overlap removal method that penalizes the overlap of dots and minimizes the sum of the penalties by using a nonlinear optimization technique. Through computational experiments with real world data, we show that our optimization-based method runs faster than an existing simulation-based method and generates dot patterns with comparable quality.