Optimization of Linear Discrete Systems An Approach to the Staircase Problem
Optimization of Linear Discrete Systems An Approach to the Staircase Problem
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To quickly assess the difficulty of the text, read a short excerpt:
Assuming that we are given an objective function separable over time, we have to deal with infinite sequences. Two alternatives are open.
1) Introduce a discount factor such that any considered sequence will converge.
2) Use the criteria of optimality suggested by Gale.
* a) A program x is said to be strongly optimal if it overtakes any other program, i. E. For the minimization case N * * Z[c(x)-c(x)]>0 V N>N t^ n n n n — — * b) A program x is said to be optimal if it catches up any othe progra...m, i. E. In the minimization case 17 V e>0, 3T s. T.
E[c (x^) - c (x^)] > - e N > T . Nn nn — — e When dealing with such infinite horizon program, one has to be very careful for there does not necessarily exist an optimal program. A very good example of this phenomenon is provided by Gale with the sharing of a pie and a utility function c = c which is convex. Let e. = ( ^' 7. -.. Ao.... , o, ... ) n n n n n times The sequence (e } gives an increasing return and nevertheless, for z the uniform convergence topology converges toward (0, .
What to read after Optimization of Linear Discrete Systems An Approach to the Staircase Problem?
You can find similar books in the "Read Also" column, or choose other free books by Hubert Tavernier to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Assuming that we are given an objective function separable over time, we have to deal with infinite sequences. Two alternatives are open.
1) Introduce a discount factor such that any considered sequence will converge.
2) Use the criteria of optimality suggested by Gale.
* a) A program x is said to be strongly optimal if it overtakes any other program, i. E. For the minimization case N * * Z[c(x)-c(x)]>0 V N>N t^ n n n n — — * b) A program x is said to be optimal if it catches up any othe progra...m, i. E. In the minimization case 17 V e>0, 3T s. T.
E[c (x^) - c (x^)] > - e N > T . Nn nn — — e When dealing with such infinite horizon program, one has to be very careful for there does not necessarily exist an optimal program. A very good example of this phenomenon is provided by Gale with the sharing of a pie and a utility function c = c which is convex. Let e. = ( ^' 7. -.. Ao.... , o, ... ) n n n n n times The sequence (e } gives an increasing return and nevertheless, for z the uniform convergence topology converges toward (0, .
What to read after Optimization of Linear Discrete Systems An Approach to the Staircase Problem?
You can find similar books in the "Read Also" column, or choose other free books by Hubert Tavernier to read onlineMoreLess
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