scholarly journals Postoptimal analysis of a linear program under simultaneous changes in matrix coefficients

1985 ◽  
pp. 1-13 ◽  
Author(s):  
Robert M. Freund
Keyword(s):  
Linear Program ◽  
Matrix Coefficients

scholarly journals On some aspects of the matrix data perturbation in linear program

2003 ◽  
Vol 13 (2) ◽  
pp. 153-164 ◽  
Author(s):  
Margita Kon-Popovska
Keyword(s):  
Linear Program ◽  
Linear Functions ◽  
Basic Solution ◽  
System Matrix ◽  
Data Perturbation ◽  
Matrix Coefficients ◽  
The Matrix ◽  
Base Matrix ◽  
Technology Resources ◽  
Optimal Basic Solution

Linear program under changes in the system matrix coefficients has proved to be more complex than changes of the coefficients in objective functions and right hand sides. The most of the previous studies deals with problems where only one coefficient, a row (column), or few rows (columns) are linear functions of a parameter. This work considers a more general case, where all the coefficients are polynomial (in the particular case linear) functions of the parameter tT??R. For such problems, assuming that some non-singularity conditions hold and an optimal base matrix is known for some particular value t of the parameter, corresponding explicit optimal basic solution in the neighborhood of t is determined by solving an augmented LP problem with real system matrix coefficients. Parametric LP can be utilized for example to model the production problem where, technology, resources, costs and similar categories vary with time. .

scholarly journals Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Gradient Descent ◽  
Main Idea ◽  
Full Column Rank ◽  
Minimum Error ◽  
Matrix Coefficients ◽  
Special Cases ◽  
Efficiency And Effectiveness ◽  
Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

scholarly journals Discrete-Time Constrained Average Stochastic Games with Independent State Processes

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1089
Author(s):  
Wenzhao Zhang
Keyword(s):  
Discrete Time ◽  
Stochastic Games ◽  
Transition Probability ◽  
Existence Condition ◽  
Linear Program ◽  
Global Minimizer ◽  
Independent State ◽  
Occupation Measures ◽  
Best Response ◽  
Mathematic Program

In this paper, we consider the discrete-time constrained average stochastic games with independent state processes. The state space of each player is denumerable and one-stage cost functions can be unbounded. In these game models, each player chooses an action each time which influences the transition probability of a Markov chain controlled only by this player. Moreover, each player needs to pay some costs which depend on the actions of all the players. First, we give an existence condition of stationary constrained Nash equilibria based on the technique of average occupation measures and the best response linear program. Then, combining the best response linear program and duality program, we present a non-convex mathematic program and prove that each stationary Nash equilibrium is a global minimizer of this mathematic program. Finally, a controlled wireless network is presented to illustrate our main results.

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