O jednom důkazu principu duality v lineárním programování
On a bicriteria optimal production plan
On cycling in the simplex method of the transportation problem
This paper shows that cycling of the simplex method for the m × n transportation problem where k-1 zero basic variables are leaving and reentering the basis does not occur once it does not occur in the k × k assignment problem. A method to disprove cycling for a particular k is applied for k=2,3,4,5 and 6.
On Farkas-type theorems
On Finite Termination in the Primal-Dual Method for Linear Programming
On first experiences with the implementation of a Newton based linear programming approach.
On gradient simplex methods for linear programs.
On hardly linearly provable systems
A well-known theorem of Rabin yields a dimensional lower bound on the width of complete polynomial proofs of a system of linear algebraic inequalities. In this note we investigate a practically motivated class of systems where the same lower bound can be obtained on the width of almost all (noncomplete) linear proofs. The proof of our result is based on the Helly Theorem.
On interior-point methods and simplex method in linear programming.
On Khachian's Algorithm and Minimal Ellipsoids.
On Nonnegative Solutions of Random Systems of Linear Inequalities.
On polyhedral games
On some Aspects of the Matrix Data Perturbation in Linear Program
On some polynomial solvable cases of the generalized minimum spanning tree problem.
On stable least squares solution to the system of linear inequalities
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable...
On the application of parallel architectures to a class of operations research problems
On the Complexity of Polyhedral Separability.
On the monotone upper bound problem.
On the Morávek and Vlach conditions for the existence of a solution to the multi-index problem
On the Properties of Linear Programming models for National Planning