Internet of Things(IoT) concept is growing in last few years and number of IoT devices is increasing rapidly. Consequently, the amount of data being collected and stored is increasing, which leads to Big data and its related challenges such as high energy consumption. While individual IoT sensors consume relatively small amount of energy, they are mostly battery powered and numerous, which limits their lifetime and creates a great load on the backend systems, respectively. In this paper, existing research work related to IoT and Big data concepts is surveyed and presented, with the focus on data velocity and volume reduction, while preserving value and variety of data. The work is categorized and structured to differentiate relevant research fields and key points within the IoT system where Big data optimization can be done. The system includes a complete data path from end-point sensors, through network of gateways, to the backend cloud and its users. The paper covers different approaches to Big data optimization in IoT, common contributions and open challenges and research questions.