A COMPARISON OF PRIMAL AND DUAL METHODS OF LINEAR PROGRAMMING

1966 ◽  
Author(s):  
Victor Klee
Keyword(s):  
Linear Programming ◽  
Dual Methods ◽  
Primal And Dual

Algorithm for Spatial Straightness Evaluation Using Theories of Linear Complex Chebyshev Approximation and Semi-infinite Linear Programming

2005 ◽  
Vol 128 (1) ◽  
pp. 167-174 ◽  
Author(s):  
LiMin Zhu ◽  
Ye Ding ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Chebyshev Approximation ◽  
Approximation Problem ◽  
Linear Complex ◽  
Infinite Linear Programming ◽  
Minimum Zone ◽  
Effectiveness And Efficiency ◽  
Primal And Dual ◽  
Straightness Error ◽  
Infinite Linear

This paper presents a novel methodology for evaluating spatial straightness error based on the minimum zone criterion. Spatial straightness evaluation is formulated as a linear complex Chebyshev approximation problem, and then reformulated as a semi-infinite linear programming problem. Both models for the primal and dual programs are developed. An efficient simplex-based algorithm is employed to solve the dual linear program to yield the straightness value. Also a general algebraic criterion for checking the optimality of the solution is proposed. Numerical experiments are given to verify the effectiveness and efficiency of the presented algorithm.

An Extended Programming Experience

1981 ◽  
Vol 13 (1) ◽  
pp. 19-27 ◽  
Author(s):  
B Harris
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Dual Methods ◽  
Solution Methods ◽  
Research Problems ◽  
Computational Aspects ◽  
Standard Solution ◽  
Order Bounds

The paper summarizes a twenty-year experience with the computational aspects of the transportation problem of linear programming. The problem is completely described and standard solution methods are summarized. The order bounds for these computations are examined. Attention then turns to some sample research problems, including shortening the search for a move, solving a condensed problem, choosing a starting basis, and several recently developed dual methods. Brief reference is made to the difficulties which arise in publishing unorthodox approaches such as those discussed in the paper.

scholarly journals Dual Approach in the Application of Geometric Interpretation of Linear Programming on the Organisation of Goods Distribution

2021 ◽  
Vol 33 (6) ◽  
pp. 847-858
Author(s):  
Bogdan Marković ◽  
Milan Marković
Keyword(s):  
Linear Programming ◽  
Geometric Interpretation ◽  
Manufacturing Companies ◽  
Mathematical Aspect ◽  
Calculation Methods ◽  
Dual Approach ◽  
The Core ◽  
Primal And Dual ◽  
Core Activity ◽  
Research Studies

The topic of the paper is the application of dual approach in formulation and resolution of goods distribution tasks problems. The gap in previous goods distribution research is the absence of the methodologies and goods transportation calculation methods for manufacturing companies with not too large amount of goods distribution whereby goods distribution is not the core activity. The goal of this paper is to find a solution for transportation in such companies. In such cases it is not rational to procure a specific software for the improvement of goods transportation but rather apply the calculation presented in this paper. The aim of this paper from mathematical aspect is to show the convenience of switching from the basic geometric interpretation of linear programming applied on transportation tasks to dual approach for the companies with too many costs limitations per transport task but not enough available transportation means. Recent research studies that use dual approach in linear programming are generally not applied to transportation tasks although such approach is very convenient. The goal of the paper is also to resolve transportation tasks by both primal and dual approach in order to prove the correctness of the method.

scholarly journals A primal-dual exterior point algorithm for linear programming problems

2009 ◽  
Vol 19 (1) ◽  
pp. 123-132 ◽  
Author(s):  
Nikolaos Samaras ◽  
Angelo Sifelaras ◽  
Charalampos Triantafyllidis
Keyword(s):  
Linear Programming ◽  
Computational Study ◽  
Optimal Solution ◽  
Simplex Algorithm ◽  
Dual Algorithm ◽  
Optimal Linear ◽  
Primal Dual ◽  
Primal And Dual ◽  
Two Phases ◽  
Feasible Solutions

The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

Primal and Dual Methods in Structural Optimization

1980 ◽  
Vol 106 (5) ◽  
pp. 1117-1133
Author(s):  
C. Fleury ◽  
Lucien A. Schmit
Keyword(s):  
Structural Optimization ◽  
Dual Methods ◽  
Primal And Dual
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