An estimate of the convergence rate for the linear programming quasisolution method
The author considers the linear programming problem \(f(x)=<c,x>\to \inf\), \(x\in X\), where X is a polyhedron described by \(X=(x\in R^ n_+:\) \(<a_ i,x>\leq b_ i\), \(i=1,...,m\); \(<a_ i,x>=b_ i\), \(i=m+1,...,s).\) When instead of the data c, \(a_ i\) and \(b_ i\), \(i=1,2,...,s\), some approximations are given, then the problem may become unstable in general. Therefore the linear programming problem must first be regularized. Such a regularization method of the quasisolutions is proposed. The stabilizing function chosen in the article is \(\Omega (x)=x_ 1+x_ 2+...+x_ n\), \(x\in R^ n_+\).
scientific article; zbMATH DE number 4213736