A Modification of Revised Simplex Method
A necessity measure optimization approach to linear programming problems with oblique fuzzy vectors
In this paper, a necessity measure optimization model of linear programming problems with fuzzy oblique vectors is discussed. It is shown that the problems are reduced to linear fractional programming problems. Utilizing a special structure of the reduced problem, we propose a solution algorithm based on Bender’s decomposition. A numerical example is given.
A New and Constructive Proof of Two Basic Results of Linear Programming
A New Exterior Point Algorithm for Linear Programming Problems
A new method for nonsmooth convex optimization.
A new parameterized logarithmic kernel function for linear optimization with a double barrier term yielding the best known iteration bound
In this paper, we propose a large-update primal-dual interior point algorithm for linear optimization. The method is based on a new class of kernel functions which differs from the existing kernel functions in which it has a double barrier term. The investigation according to it yields the best known iteration bound for large-update algorithm with the special choice of its parameter and thus improves the iteration bound obtained in Bai et al. [El Ghami2004] for large-update algorithm.
A non improving simplex algorithm for transportation problems
A note on the solution of integer linear programming problems using duality properties
A numerical feasible interior point method for linear semidefinite programs
This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.
A numerically stable least squares solution to the quadratic programming problem
The strictly convex quadratic programming problem is transformed to the least distance problem - finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS...
A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization
In this paper we propose a primal-dual interior-point algorithm for convex quadratic semidefinite optimization problem. The search direction of algorithm is defined in terms of a matrix function and the iteration is generated by full-Newton step. Furthermore, we derive the iteration bound for the algorithm with small-update method, namely, O( log ), which is best-known bound so far.
A Primal-Dual Exterior Point Algorithm for Linear Programming Problems
A procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem
A remark on sensitivity in linear programming and Gale-Samuelson nonsubstitution theorem
A Slight Modification of the First Phase of the Simplex Algorithm
A topology over a set of systems
The systems of an arbitrary number of linear inequalities OVer a real locally convex space have been classified in three classes, namely: consistent, weakly inconsistent and strongly inconsistent, i.e. having ordinary solutions, weak solutions or notsolutions respectively. In this paper, the third type is divided in two classes: strict-strongly and quasi-strongly inconsistent and is given a topology over a quotient space of the set of systems over finite- dimensional spaces, that yields a set of...
A Two-Phase Linear Programming Approach for Redundancy Allocation Problems
A View of Interior Point Methods for Linear Programming
Achievable potential reductions in the method of Kojima et al. in the case of linear programming
Algorithm 51. Solution of linear programming problems in zero-one variables