An Interior Linear Programming Algorithm Using Local and Global Knowledge

1988 ◽  
Vol 110 (1) ◽  
pp. 58-64 ◽  
Author(s):  
Heng Long Li ◽  
Panos Papalambros
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Programming Algorithm ◽  
Global Knowledge ◽  
Active Set ◽  
Active Set Strategy ◽  
Linear Programming Algorithm ◽  
Linear Programming Problems

A new algorithm for linear programming problems is presented. The algorithm makes interior moves with a special active set strategy that utilizes both local and global knowledge. This knowledge represents primarily monotonicity and dominance information. The article describes the rationale, theory, implementation, and some test examples for the algorithm. The ideas presented form the basis for nonlinear programming extensions in sequel articles.

The Performance Validation of Linear Programming Algorithm Based on Integrated Benchmark

2010 ◽  
Vol 34-35 ◽  
pp. 1794-1799
Author(s):  
Shu Hong Chen ◽  
Guo Feng Yan
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Programming Algorithm ◽  
Benchmark Analysis ◽  
Linear Programming Algorithm ◽  
Linear Programming Problems ◽  
Continuous Performance Improvement ◽  
Performance Validation ◽  
Optimizing Algorithm ◽  
Programming Algorithms

Benchmark is a method of measuring performance, and we can obtain continuous performance improvement of programming algorithm through Benchmark validation. In order to solve large-scale linear programming problems, this paper proposes an integrated Benchmark validation which integrates theoretical Benchmark analysis with advance language-based Benchmark. Through the integrated Benchmark validation, we can continuously improve an optimizing algorithm, and validate whether the new optimizing algorithm achieves the performance objectives. The results of experiments show the proposed integrated Benchmark validation is an effective method for developing large-scale linear programming algorithms.

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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