Fundamentals of a Continuous Time Simplex Method.
STANFORD UNIV CALIF SYSTEMS OPTIMIZATION LAB
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Continuous linear programs have wide applicability as models of many real world situations that are intertemporal in nature. An important special case is the all linear optimal control problem with mixed state and control variable constraints. This dissertation considers generalizations of the techniques of linear programming to solve continuous linear programs with constant coefficients. A characterization of extreme points is obtained in terms of certain full rank conditions. Such solutions are called basic feasible solutions. Then a statement of the optimality conditions is presented in a framework that is free of the delta functional and its derivatives. This is followed by the major part of the dissertation which is a means of obtaining descent by moving along a continuous path of extreme points.
- Theoretical Mathematics