Abstract

This paper deals with the problem of sensitivity analysis in calculus of variations. A perturbation technique is applied to derive the boundary value problem and the system of equations that allow us to obtain the partial derivatives (sensitivities) of the objective function value and the primal and dual optimal solutions with respect to all parameters. Two examples of applications, a simple mathematical problem and a slope stability analysis problem, are used to illustrate the proposed method.

Highlights

  • Today, users are not satisfied with just the solutions to given problems and require knowledge of how and how much these solutions depend on data

  • Sensitivity analysis in calculus of variations can be considered to be a byproduct of results on second order conditions in optimization problems in general or on some particular cases of optimal control

  • In this paper we try to head in this direction as we deal with calculus of variations, developing a general technique for obtaining the sensitivities of the objective function optimal value, the dual variable values or functions, and the optimal solution with respect to real data, parameters, or data functions

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Summary

Introduction

Users are not satisfied with just the solutions to given problems and require knowledge of how and how much these solutions depend on data. Sensitivity analysis in calculus of variations can be considered to be a byproduct of results on second order conditions in optimization problems in general (see [1]) or on some particular cases of optimal control.

Results
Conclusion

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