  We introduce a method for solving the "inverse" phase equilibria problem: How
should the interactions among a collection of molecular species be designed in
order to achieve a target phase diagram? Using techniques from convex
optimization theory, we show how to solve this problem for phase diagrams
containing a large number of components and many coexisting phases with
prescribed compositions. We apply our approach to commonly used mean-field
models of multicomponent fluids and then use molecular simulations to verify
that the designed interactions result in the target phase diagrams. Our
approach enables the rational design of "programmable" fluids, such as
biopolymer and colloidal mixtures, with complex phase behavior.
