Modern optimization theory and applications

Over the past a few decades, significant progress has been made in the field of operations research, particularly in optimization theory and its applications. This article intensively investigates many subjects in this field, such as linear programming, nonlinear programming, online optimization, machine learning, combinatorial optimization, integer programming, mechanism design, inventory management, revenue management, etc. This survey paper does not intend to provide an encyclopedic review for the whole field, but rather focuses more on mainstream methodology, research framework, and the newest advances of some important subjects. It particularly emphasizes several recent interesting and meaningful discoveries,which potentially stimulates more quality research in the field.