Various tasks in data science, including signal processing and machine learning, can be effectively tackled by leveraging both a priori information of the target to be estimated and mathematical properties underlying these tasks. Based on this fundamental principle, we introduce mathematical models for the various tasks as innovative optimization problems and develop powerful algorithms. Our objective is to apply these research outcomes in engineering for practical solutions. Our research interests include but are not limited to: ・Machine learning models and their learning algorithms ・Optimization models for audio/image signal processing ・Sparse signal processing ・Algorithms for convex optimization ・Tensor decomposition for data analysis