The inverse problem for standard linear programming problems
The inverse problem for standard linear programming ones (SLPP) is solved. More exactly, fix a (matrix) triplet \((A,b,C)\) of the coefficients which determines a SLPP, and suppose that the corresponding canonical problem has a nondegenerate support optimal solution \(X_0\in \mathbb{R}^{n+m}\). The problem is to find the set of all canonical problems such that the first \(n\) coordinates of their nondegenerate basis optimal solutions equal the corresponding coordinates of \(X_0\). Three cases are considered depending on the structure (the number of positive coordinates) of the optimal solution \(X_0\). For each case the desired set (that equals the set of all SLPP with the optimal solution) is constructed in the explicit form and is parametrized by the given coefficients.
scientific article; zbMATH DE number 1557727