This paper discusses the nature of optimal solutions for a class of continuouslinear programs called separated continuouslinear programs. It is shown that under various different assumptions on the problem data ther...
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This paper discusses the nature of optimal solutions for a class of continuouslinear programs called separated continuouslinear programs. It is shown that under various different assumptions on the problem data there exist optimal solutions that are piecewise constant, piecewise polynomial, or, more generally, piecewise analytic. These results are reminiscent of bang-bang results in linear optimal control.
Shortest path problems are considered for a graph in which edge distances can vary with time, each edge has a transit time, and parking (with a corresponding penalty) is allowed at the vertices. The problem is formula...
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Shortest path problems are considered for a graph in which edge distances can vary with time, each edge has a transit time, and parking (with a corresponding penalty) is allowed at the vertices. The problem is formulated an a continuous-time linear program, and a dual problem is derived for which the absence of a duality gap is proved. The existence of an extreme-point solution to the continuous-time linear program is also demonstrated, and a correspondence is derived extreme points and continuous-time shortest paths. Strong duality is then derived in the case where the edge distances satisfy a Lipschitz condition.
The link between the Euler equations of perfect incompressible flows and the Least Action Principle has been known for a long time [1]. Solutions can be considered as geodesic curves along the manifold of volume prese...
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This paper briefly reviews the literature on necessary optimality conditions for optimal control problems with state-variable inequality constraints. Then, it attempts to unify the treatment of linear optimal control ...
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This paper briefly reviews the literature on necessary optimality conditions for optimal control problems with state-variable inequality constraints. Then, it attempts to unify the treatment of linear optimal control problems with state-variable inequality constraints in the framework of continuous linear programming. The duality theory in this framework makes it possible to relate the adjoint variables arising in different formulations of a problem; these relationships are illustrated by the use of a simple example. This framework also allows more general problems and admits a simplex-like algorithm to solve these problems.
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