Sensitivity Analysis in Linear and Nonlinear Programming Models
| dc.contributor.advisor | Mitiku Semu (PhD) | |
| dc.contributor.author | Sisay Aragaw | |
| dc.date.accessioned | 2020-12-17T06:59:43Z | |
| dc.date.accessioned | 2023-11-04T12:31:09Z | |
| dc.date.available | 2020-12-17T06:59:43Z | |
| dc.date.available | 2023-11-04T12:31:09Z | |
| dc.date.issued | 2015-07-07 | |
| dc.description.abstract | Sensitivity analysis shows how the optimal solution and the value of its ob- jective function change, given changes in various inputs to the problem. The task of sensitivity analysis is to _nd out the change limits of data, in other words the stable interval, so that optimal solution or optimal basis will remain within its range of optimality. The solution of the optimization problem is terminated when it reaches a minimum value subject to the given constraints. If the solution belongs to the boundary of some constraint, such constraints are called active and the impact of these active constraints on the solution could be found by acquiring the Lagrange multiplier associated with these constraints. Since the solution is optimal,the Lagrange multipliers associ- ated with inequality constraints have nonnegative values [7]. To understand how sensitive is the optimal solution with respect to the small change in the right-hand side of the active constraints, the constraints are perturbed and the new so-obtained optimization problem is solved. The sensitivity analysis provides information for both linear and nonlin- ear programming problems, including dual values (in both cases) and range information (for linear problems only). The dual values for (nonbasic) vari- ables are called reduced Costs in the case of linear programming problems, and reduced gradients for nonlinear problems.The dual values for (binding) constraints are called Shadow Prices for linear programming problems, and Lagrange Multipliers for nonlinear problems. The active constraints are not assumed to remain active if the problem data are perturbed, nor the partial derivatives are assumed to exist. In other words, all the elements, variables, parameters, KKT multipliers, and objective function values may vary pro- vided that optimality is maintained and the general structure of a feasible perturbation. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/24154 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Sensitivity | en_US |
| dc.subject | Analysis in Linear | en_US |
| dc.subject | Nonlinear | en_US |
| dc.subject | Programming Models | en_US |
| dc.title | Sensitivity Analysis in Linear and Nonlinear Programming Models | en_US |
| dc.type | Thesis | en_US |