Modified simplex imbeddings method in convex non-differentiable optimization
We consider a new interpretation of the modified simplex imbeddings method. The main construction of this method is a simplex which contains a solution of convex non-differentiable problem. A cutting plane drawn through the simplex center is used to delete a part of the simplex without the solution. The most interesting feature of this method is the convergence estimation which depends only on the quantity of simplex vertices that are cut off by the cutting hyperplane. The more vertices are cut off by the cutting hyperplane, the higher rate of method convergence. We consider the special technique of constructing the simplex containing the set of points defining the truncated simplex. Such approach let us attribute the problem of constructing the minimal volume simplex to structural optimization problems that have quite efficient interior-point schemes for finding the optimal solution. The results of numerical experiment are also given in this paper. Copyright © by the paper's authors.
Библиографическая ссылка
Kolosnitcyn A. Modified simplex imbeddings method in convex non-differentiable optimization // CEUR Workshop Proceedings. Vol.1623. 2016. P.226-233.
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