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A similar decomposition can be applied to sigmoid utility functions, transforming problem (1) into: U tot ∗ = max p ∈ A, d ∑ k = 1 K U k d k s.t.
To obtain conditions (11)–(13) when q is only required to be well-behaved, our strategy will consist in transforming Problem 2 into another program, suitable to be treated under the current methods of control theory.
It should be emphasized on the other hand that no advanced optimization technique is required for the derivation of the Theorem, provided the procedure in the Appendix just consists in transforming Problem 2 into another program where we do not have to deal directly with constraint (10) above.
Now, we consider transforming Problem A by using (20), (21), and (22).
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A method of transforming problems with diffuse interfaces is presented which leads to equations that are easier to compute accurately.
By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms.
The basic strategy of inversive methods is to transform a given Apollonius problem into another Apollonius problem that is simpler to solve; the solutions to the original problem are found from the solutions of the transformed problem by undoing the transformation.
After the transformation, to ensure the consistency of the whole transformed problem, the RPS generator propagates the modification on the CWM to the PSPM and vice versa.
Transform problem (1.1) into a fixed point problem.
We transform problem (1.1) to its equivalent integral equations.
Proof We will transform problem (1), (2) and (3) into a fixed point problem.
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