%0 Journal Article
%A Shcherbashin, Yuriy D.
%D 2006
%I Begell House
%N 5
%P 23-33
%R 10.1615/J Automat Inf Scien.v38.i5.30
%T Method of Solving Nonlinear Programming Using Variable Dimension Basis
%U http://dl.begellhouse.com/journals/2b6239406278e43e,5eb3e31424b87589,5ec0907711009bcc.html
%V 38
%X Consideration is given to approximation programming method with gradually increasing/decreasing basis dimension. If the solution is found in the vertex of limiting polyhedron, i.e., on the boundary of intersection of
n-limiting hyperplane (*n* — dimension of space of searched variables), then the basis dimension reaches *n*; if the solution is on the faces or edges of limiting polyhedron, then the basis dimension decreases. With the solution found inside the admissible domain, then the basis dimension is zero and
*X*-trace on the last steps corresponds to the fastest descent (ascent) algorithm. The other feature of the method is the application of quadratic approximation of discrepancy Δ φ_{i} (*X*) variation along admissible appropriate direction — ray σ — linear combination of edges of current basis cone. The quadratic approximation method enables us to increase the step length in comparison with the simplest methods of approximation programming.
%8 2006-08-22