Defense Applications of Mathematical Programs with Optimization Problems in the Constraints

Bracken and McGill have discussed the theory, computations, and an example of mathematical programming models with optimization problems in the constraints [Opns. Res. 21, 37–44 (1973)], and have presented a computer program for solving such models with nonlinear programs in the constraints [Opns. Res. 22, 1097–1101 (1974)]. Bracken, Falk, and McGill have given a procedure for transforming mathematical programs with two-sided optimization problems in the constraints into mathematical programs with nonlinear programs in the constraints [Opns. Res. 22, 1102–1104 (1974)], thus enabling their solution by the computer program. This paper formulates models of defense problems that are convex programs having the mathematical properties treated in the previous papers. The models include several strategic-force-planning models and two general-purpose-force planning models.