scholarly journals Lipschitz Modulus of the Optimal Value in Linear Programming

2018 ◽  
Vol 182 (1) ◽  
pp. 133-152 ◽  
Author(s):  
María Jesús Gisbert ◽  
María Josefa Cánovas ◽  
Juan Parra ◽  
Fco. Javier Toledo
Keyword(s):  
Linear Programming ◽  
Optimal Value ◽  
Lipschitz Modulus

scholarly journals Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming

2021 ◽  
Author(s):  
M. J. Cánovas ◽  
M. J. Gisbert ◽  
D. Klatte ◽  
J. Parra
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Value Function ◽  
Extreme Points ◽  
Linear Programs ◽  
Geometrical Approach ◽  
Nominal Data ◽  
Optimal Value ◽  
Lipschitz Modulus ◽  
Finite Linear

AbstractIn this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

Improved performance control on the Grid

2009 ◽  
Vol 367 (1897) ◽  
pp. 2533-2543
Author(s):  
M.E. Tellier ◽  
G.D. Riley ◽  
T.L. Freeman
Keyword(s):  
Linear Programming ◽  
Control System ◽  
Execution Time ◽  
Optimal Schedule ◽  
Threshold Value ◽  
Optimal Threshold ◽  
Performance Control ◽  
Optimal Value ◽  
Improved Performance

In the 2005 paper by Mayes et al ., a threshold-based performance control system (PerCo) was described and an initial experimental evaluation was presented. The objective of the current paper is to investigate the role of the threshold value in PerCo and to place the threshold-based rescheduling heuristic on a more principled footing. Simulation enables us to identify the ‘optimal’ threshold value for a particular application scenario, and we show that this optimal value results in a 10 per cent improvement in performance for the application considered by Mayes et al . Furthermore, we find that the execution time of this optimal threshold-based schedule is very close (within 0.5%) to the execution time that results from a linear programming optimal schedule.

scholarly journals Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Haifang Cheng ◽  
Weilai Huang ◽  
Jianhu Cai
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Compromise Programming ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Optimal Value ◽  
Fuzzy Equality

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.

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