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Gideon Weiss - A simplex-type algorithm for continuous linear programs with constant coefficients, Aug 29

Joint work with Evgeny Shindin.

ABSTRACT: We consider continuous linear programs over a continuous finite time horizon T, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the separated continuous linear programming models and their various duals, as formulated in the past by Anderson, by Pullan, and by Weiss. We formulate a symmetric dual and show that these problems possess optimal strongly dual solutions. We give a detailed description of optimal solutions and define a combinatorial analogue to basic solutions of standard LP. We present an algorithm which solves this class of problems in a finite bounded number of steps, using an analogue of the simplex method, in function space.

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