This paper offers a new standard, called MOSDEX (Mathematical Optimization Solver Data EXchange), for managing the interaction of data with solvers for mathematical optimization. The rationale for this standard is to take advantage of modern software tools that can efficiently handle very large datasets that have become the norm for data analytics in the past few years. MOSDEX is based on several principles: independence from and support for multiple optimization solvers and multiple algebraic modeling languages, separation of model and data, relational data modeling using SQL, and incorporation of standard optimization modeling artifacts. MOSDEX uses the widely adopted JSON data format standard to take advantage of JSON support in a variety of programming languages including Java, C++, Python, and Julia. The paper demonstrates the principles of MOSDEX through examples taken from a well-known optimization problem. On-line resources provide a full description of the MOSDEX syntax, a working implementation of its Reference architecture, and a library of examples of MOSDEX representations of optimization problems.