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Articles

Differential stability of convex optimization problems under inclusion constraints

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Pages 108-128 | Received 31 Oct 2013, Accepted 26 Jan 2014, Published online: 14 Mar 2014

References

  • Aubin J-P. Optima and equilibria. An introduction to nonlinear analysis. 2nd ed. New York (NY): Springer; 1998.
  • Auslender A. Differential stability in nonconvex and nondifferentiable programming. Math. Program. Study. 1979;10:29–41.
  • Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer; 2000.
  • Dien PH, Yen ND. On implicit function theorems for set-valued maps and their application to mathematical programming under inclusion constraints. Appl. Math. Optim. 1991;24:35–54.
  • Gauvin J, Dubeau F. Differential properties of the marginal function in mathematical programming. Math. Program. Study. 1982;19:101–119.
  • Gauvin J, Dubeau F. Some examples and counterexamples for the stability analysis of nonlinear programming problems. Math. Program. Study. 1984;21:69–78.
  • Gollan B. On the marginal function in nonlinear programming. Math. Oper. Res. 1984;9:208–221.
  • Mordukhovich BS, Nam NM, Yen ND. Subgradients of marginal functions in parametric mathematical programming. Math. Program. Ser. B. 2009;116:369–396.
  • Rockafellar RT. Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming. Math. Program. Study. 1982;17:28–66.
  • Thibault L. On subdifferentials of optimal value functions. SIAM J. Control Optim. 1991;29:1019–1036.
  • Ioffe AD, Tihomirov VM. Theory of extremal problems. Amsterdam: North-Holland; 1979.
  • Mordukhovich BS. Variational analysis and generalized differentiation, Volume I: Basic theory, Volume II: Applications. Berlin: Springer; 2006.
  • Bartl D. A short algebraic proof of the Farkas lemma. SIAM J. Optim. 2008;19:234–239.

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