Geodesic
Using of modified simplex imbeddings method for solving special class of~convex non-differentiable optimization problems
The Bulletin of Irkutsk State University. Series Mathematics, Tome 11 (2015), pp. 54-68

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In this paper it is considered 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 by the cutting plane, the higher speed of method convergence. Modified method of simplex imbeddings with such criteria of cutting plane choosing is applied to solving special class of convex non-differentiable problems, which is consists of two types of functions. We come across the necessity to describe the function subdifferential that is depends on one or several parameters, that we can subject to optimization. It is described functions subdifferentials from the introduced class in parametric representation, that let us form auxiliary problems in simplex imbeddings method for searching resulting cutting planes, that cut off as much vertices of simplex as possible. It let us increase the speed of finding 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. 
@article{IIGUM_2015_11_a4,
     author = {A. V. Kolosnitcyn},
     title = {Using of modified simplex imbeddings method for solving special class of~convex non-differentiable optimization problems},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {54--68},
     publisher = {mathdoc},
     volume = {11},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2015_11_a4/}
}
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A. V. Kolosnitcyn. Using of modified simplex imbeddings method for solving special class of~convex non-differentiable optimization problems. The Bulletin of Irkutsk State University. Series Mathematics, Tome 11 (2015), pp. 54-68. http://geodesic.mathdoc.fr/item/IIGUM_2015_11_a4/