The application of nonlinear programming methods to the solution of constrained saddle-point problems.

Abstract

Nonlinear programming methods are used to solve saddle-point problems subject to inequality constraints on the variables; in particular, the type of saddle-point problem arising in pursuit-evasion differential games is considered. The methods investigated fall into two groups: solution of the nonlinear simultaneous equations obtained from the Kuhn-Tucker conditions, and solution of a sequence of constrained optimization problems by the gradient projection algorithm. These methods are applicable to any real-valued function f(x,y) which is convex in x, concave in y, and has continuous and bounded second partial derivatives. Several examples are given which illustrate the characteristics of the numerical procedures .