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.

This note describes a computational procedure for solving mathematical programs with nonlinear programs in the constraints; it uses the SUMT computer program for the overall mathematical program, and a new program called INSUMT for the nonlinear programs in the constraints.

This paper formulates a convex programming model allocating submarine-launched ballistic missiles (SLBMs) to launch areas and providing simultaneously an optimal targeting pattern against a specified set of bomber bases. Flight times of missiles from launch areas to bases vary and targets decrease in value over time. A nonseparable concave objective function is given for expected destruction of bombers. An example is presented.

This paper considers a class of optimization problems characterized by constraints that themselves contain optimization problems. The problems in the constraints can be linear programs, nonlinear programs, or two-sided optimization problems, including certain types of games. The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory. It gives an application with linear programs in the constraints, and discusses computational methods for solving the problems.

Bracken and McGill have recently studied two classes of mathematical programs with optimization problems in the constraints [Opns. Res. 21, 37–44 (1973)], the first class involving mathematical programs in the constraints and the second max-min problems there. They have also developed a computational technique and shown that it is effective in solving problems of the first class [Opns. Res. 22, 1097–1101 (1974)]. This note shows that the computational technique can be applied to problems of the apparently wider second class.