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The reformulated problems can be solved by existing semi-infinite optimization algorithms and computational reliability methods.
For nonaffine limit-state functions, approximate solutions are obtained by solving series of reformulated problems.
It is shown that the reformulated problems produce solutions that are identical to those of the original problems when the limit-state functions defining the reliability problem are affine.
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Based on this reformulation, we show that the basis of the reformulated problem is closely related with the minimum cost flow problem and design a kind of network simplex method to get the integrated optimal solution of the problem.
For the reformulated problem (2.12 - 2.14), we can deduce the following result.
The first of those two solutions was found using the reformulated problem (3.8) with as the right-hand side.
The reformulated problem was an optimisation problem involving spectral radius constraint sets, and optimal solutions were obtained by using a tuning-free geometrically fast convergent algorithm.
An iterative algorithm based on the bisection method is proposed to solve the relaxed version (relaxed the non-convex rank constraints in the problem) of the reformulated problem.
And then, we propose an EE-Max algorithm coupled with the Max-SINR, nonlinear fraction programming and one dimension searching to solve the reformulated problem.
This system is described by a measure-driven inclusion (which is a reformulated problem from [50]) d x ∈ F ( x ) d x + G ( x ) d μ d ( x ).
PSO is used to solve the reformulated problem and priority ranking of constraint fitness is proposed to guarantee that the constraints are satisfied.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com