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The optimization problem based on robust design is solved by SDP and interior method.
With the fixed, optimize the following convex problem by using the interior method of convex optimizations to obtain : (20).
Firstly, we apply the convex optimization to getting over the problem ((mathcal {SP}1)) based on the interior method.
While the bound in (46) is not tight, applying the interior method to solve (46) as suggested in [27] is not computationally efficient.
Step 4. With the fixed solve the following convex problem by optimizing and simultaneously with the interior method to attain (21).
Thus, many convex optimization methods such as the interior method and the Lagrangian multiplier method can be employed to solve (17).
Similar(51)
Both Robust-LPM and the relaxed Robust-SP can be efficiently solved by interior methods, practically using a software like CVX.
We should mention that our approach can be used to extend many interior methods which are associated with polyhedral feasible regions, e.g., the algorithms given by [3, 4].
In [7] Bank et al. consider the application of primal-dual interior methods to the optimization of systems arising in the finite-element discretization of a class of elliptic variational inequalities.
When interior methods are applied to the discretized problem, the resulting linear systems have the same zero/nonzero structure as the finite-element equations solved for the unconstrained case.
Note that best response problem (15) and (30) are both convex and thus can be solved very efficiently using standard convex optimization methods (interior point method, for one) [17].
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