A new linear programming algorithm — better or worse than the Simplex Method?

1980 ◽  
Vol 2 (3) ◽  
pp. 141-146 ◽  
Author(s):  
L. Lovász
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Programming Algorithm ◽  
Linear Programming Algorithm

scholarly journals A linear programming algorithm to test for jamming in hard-sphere packings

2004 ◽  
Vol 197 (1) ◽  
pp. 139-166 ◽  
Author(s):  
Aleksandar Donev ◽  
Salvatore Torquato ◽  
Frank H. Stillinger ◽  
Robert Connelly
Keyword(s):  
Linear Programming ◽  
Hard Sphere ◽  
Programming Algorithm ◽  
Sphere Packings ◽  
Linear Programming Algorithm

A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design

1988 ◽  
Author(s):  
Y. Wang ◽  
E. Sandgren
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Inequality Constraints ◽  
Upper And Lower Bounds ◽  
Programming Algorithm ◽  
Active Constraint ◽  
Design Variables ◽  
Artificial Variable ◽  
Linear Programming Problems ◽  
Revised Simplex Method

Abstract A new linear programming algorithm is proposed which has significant advantages compared to the traditional simplex method. The search direction generated which is always along a common edge of the active constraint set, is used to locate candidate constraints, and can be used to modify the current basis. The dimension of the basis begins at one and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared with a traditional revised simplex method.

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