Algebraic modeling languages like AIMMS, AMPL, GAMS, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other.
Researchers are constantly updating the types of problems and algorithms that they wish to use to model in specific domain applications.
The new types of problems modeled with EMP are reformulated with the GAMS solver JAMS to well established types of problems and the reformulated models are passed to a suitable GAMS solver to be solved.
The core of EMP is a file called emp.info where the annotations that are needed for the reformulations are added to the model.
Equilibrium problems model questions arising in the study of economic equilibria in a mathematically abstract form.
Examples of the use of EMP to solve equilibrium problems include the computation of Cournot–Nash–Walras equilibria..,[1] modeling water allocation,[2][3] long-term planning of transmission line expansion of the electrical grid,[4] modeling risk-averse agents in hydro-thermal electricity markets with uncertain inflows into hydro reservoirs [5] and modeling variational inequalities in energy markets [6] Hierarchical optimization problems are mathematical programs with an additional optimization problem in their constraints.
Disjunctive programs have many applications, including ordering of tasks in a production process, organizing complex projects in a time saving manner and choosing the optimal route in a circuit.