Directional derivatives of the solution of a parametric nonlinear program

  title={Directional derivatives of the solution of a parametric nonlinear program},
  author={Daniel Ralph and Stephan Dempe},
  journal={Math. Program.},
Consider a parametric nonlinear optimization problem subject to equality and inequality constraints. Conditions under which a locally optimal solution exists and depends in a continuous way on the parameter are well known. We show, under the additional assumption of constant rank of the active constraint gradients, that the optimal solution is actually piecewise smooth, hence B-differentiable. We show, for the first time to our knowledge, a practical application of quadratic programming to… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 28 references

Sensitivity analysis of nonlinear programs and differentiability properties of metric projections

  • A. Shapiro
  • SIAM Journal on Control and Optimization 26 (1988…
  • 1988
Highly Influential
11 Excerpts

Structural analysis of nonsmooth mappings, inverse functions, and metric projections

  • L. Kuntz, S. Scholtes
  • Journal of MathematicaI Analysis and Applications…
  • 1994
1 Excerpt

Directional derivatives of optimal solutions in smooth nonlinear programming

  • J. F. Bonnans
  • Journal of Optimization Theory and Applications…
  • 1992
1 Excerpt

Drveloppement de solutions exactes et approchres en programmation non linraire

  • J. F. Bonnans, A. D. Ioffe, A. Shapiro
  • Comptes Rendus de l'Acad£mie des Sciences Paris…
  • 1992
3 Excerpts

Expansion of exact and approximate solutions in nonlinear programming

  • J. F. Bonnans, A. D. Ioffe, A. Shapiro
  • in: W. Oetlli and D. Pallaschke, eds., Advances…
  • 1992
3 Excerpts

Perturbation analysis of optimization problems in Banach spaces

  • A. Shapiro
  • Numerical Functional Analysis and Optimization 13…
  • 1992
1 Excerpt

Sensitivity analysis of parameterized programs under cone constraints

  • A. Shapiro, J. F. Bonnans
  • SIAM Journal on Control and Optimization 30 (1992…
  • 1992
1 Excerpt

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