Sensitivity Analysis In Linear And Nonlinear Programming Models

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Sensitivity analysis shows how the optimal solution and the value of its ob-rnjective function change, given changes in various inputs to the problem. Therntask of sensitivity analysis is to _nd out the change limits of data, in otherrnwords the stable interval, so that optimal solution or optimal basis will remainrnwithin its range of optimality. The solution of the optimization problem isrnterminated when it reaches a minimum value subject to the given constraints.rnIf the solution belongs to the boundary of some constraint, such constraintsrnare called active and the impact of these active constraints on the solutionrncould be found by acquiring the Lagrange multiplier associated with thesernconstraints. Since the solution is optimal,the Lagrange multipliers associ-rnated with inequality constraints have nonnegative values [7]. To understandrnhow sensitive is the optimal solution with respect to the small change in thernright-hand side of the active constraints, the constraints are perturbed andrnthe new so-obtained optimization problem is solved.rnThe sensitivity analysis provides information for both linear and nonlin-rnear programming problems, including dual values (in both cases) and rangerninformation (for linear problems only). The dual values for (nonbasic) vari-rnables are called reduced Costs in the case of linear programming problems,rnand reduced gradients for nonlinear problems.The dual values for (binding)rnconstraints are called Shadow Prices for linear programming problems, andrnLagrange Multipliers for nonlinear problems. The active constraints are notrnassumed to remain active if the problem data are perturbed, nor the partialrnderivatives are assumed to exist. In other words, all the elements, variables,rnparameters, KKT multipliers, and objective function values may vary pro-rnvided that optimality is maintained and the general structure of a feasiblernperturbation.

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Sensitivity Analysis In Linear And Nonlinear Programming Models

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