New trajectory-following polynomial-time algorithm for linear programming problems

1989 ◽  
Vol 63 (3) ◽  
pp. 433-458 ◽  
Author(s):  
C. Roos
Keyword(s):  
Linear Programming ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Linear Programming Problems ◽  
Trajectory Following

scholarly journals On the exact polynomial time algorithm for a special class of bimatrix game

2013 ◽  
Vol 54 ◽  
Author(s):  
Jonas Mockus ◽  
Martynas Sabaliauskas
Keyword(s):  
Game Theory ◽  
Linear Programming ◽  
Nash Equilibrium ◽  
Polynomial Time ◽  
Explicit Solution ◽  
Special Class ◽  
Polynomial Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Bimatrix Game

The Strategy Elimination (SE) algorithm was proposed in [2] and implemented by a sequence of Linear Programming (LP) problems. In this paper an efficient explicit solution is developed and the convergence to the Nash Equilibrium is proven.Keywords: game theory, polynomial algorithm, Nash equilibrium.

scholarly journals An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Bo Zhang ◽  
YueLin Gao ◽  
Xia Liu ◽  
XiaoLi Huang
Keyword(s):  
Polynomial Time ◽  
Outer Space ◽  
Optimal Solution ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Acceleration Technique ◽  
Region Division ◽  
Positive Exponent ◽  
Linear Programming Problems ◽  
Multiplicative Programs

This paper explains a region-division-linearization algorithm for solving a class of generalized linear multiplicative programs (GLMPs) with positive exponent. In this algorithm, the original nonconvex problem GLMP is transformed into a series of linear programming problems by dividing the outer space of the problem GLMP into finite polynomial rectangles. A new two-stage acceleration technique is put in place to improve the computational efficiency of the algorithm, which removes part of the region of the optimal solution without problems GLMP in outer space. In addition, the global convergence of the algorithm is discussed, and the computational complexity of the algorithm is investigated. It demonstrates that the algorithm is a complete polynomial time approximation scheme. Finally, the numerical results show that the algorithm is effective and feasible.

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