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USING OF PARAMETRIC REPRESENTATION OF SUBDIFFERENTIAL IN MODIFIED SIMPLEX IMBEDDINGS METHOD

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We consider the modified simplex imbeddings method, which is related to the class of cutting plane methods. The main feature of this method is the convergence estimation, which depends only on the quantity of simplex vertices, that are cut off by the cutting plane. The more vertices are cut off the higher speed of method convergence. This estimation let us obtain the criteria of cutting plane choosing, that provide better speed of method convergence and form modification of simplex imbeddigs method. The modified method is applied to solving special class of convex non-differentiable problems. Then we describe the functions subdifferentials that are depend on several parameters. It let us form auxiliary problems for searching resulting cutting planes, that cut off as much vertices of simplex as possible and increase the speed of finding of optimal solution. The results of numerical experiment are also given in this paper.

Keywords

modified simplex imbeddings method; subdifferential of convex functions; resulting cutting plane

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UDC

519.853.3

Pages

1209-1214

References

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Received

2015-05-07

Section of issue

Scientific articles

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