Maximum descent monotone solutions of an ordinary differential equation with a discontinuous right-hand side |
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Authors: | M Falcone A Siconolfi |
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Institution: | 1. Istituto di Matematica G. Castelnuovo, Università di Roma, Roma, Italy 2. Dipartimento di Matematica, Università della Calabria, Arcavacata di Rende, Cosenza, Italy
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Abstract: | We present an existence theorem for absolutely continuous monotone solutions of the Cauchy problem $$\dot x\left( t \right) = proj_{T_{P\left( {x\left( t \right)} \right)} x\left( t \right)} ( - \nabla w(x)(t))),x\left( 0 \right) = x_0 .$$ Moreover, we prove that the limit pointx* of any solution is a minimum forw(·) inP(x*). The results are applied to a decision problem for a firm which wants to satsify twoa priori incompatible criteria: (i) monotonicity with respect to a preorder; and (ii) minimization of costs. |
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