OPTIMIZATION PROBLEMS IN MASS TRANSPORTATION THEORY ...
OPTIMIZATION PROBLEMS IN MASS TRANSPORTATION THEORY ...
OPTIMIZATION PROBLEMS IN MASS TRANSPORTATION THEORY ...
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The function B can be seen as a control variableand the corresponding transport planas a state variable, so that the optimizationproblem we consider:min { F (B) : B l.s.c. increasing, B(0) = 0 }can be seen as an optimal control problem.Theorem There exists an optimal pricingpolicy B opt solving the maximal incomeproblem above.Also in this case some necessary conditionsof optimality can be obtained. In particular,the function B opt turns out to be continuous,and its Lipschitz constant can bebounded by the one of A (the function measuringthe own means cost).33