Abstract: Mathematical programming or mathematical optimization is an important branch of operations research that studies the problem of minimizing or maximizing a real function of real or integer variables,  subject to constraints on the variables.  It is one of widely used modeling tools and methodologies in operations research and management science and has numerous applications in engineering, economics and finance.  In this chapter,  we first give a brief introduction of mathematical programming problems, its history, applications and main research areas.  We then review the state-of-the-science of mathematical programming study with an overview of the development of mathematical programming in China.  Research perspectives of mathematical programming is also presented.

Key words: mathematical programming, optimization, overview of mathematical programming in China, state-of-the-science of mathematical programming, research outlook