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second-order derivative; $C^{1,1}$ function; stable function; isolated minimizer of order 2
The aim of our article is to present a proof of the existence of local minimizer in the classical optimality problem without constraints under weaker assumptions in comparisons with common statements of the result. In addition we will provide rather elementary and self-contained proof of that result.
[BP1] Bednařík D., Pastor K.: Elimination of strict convergence in optimization. SIAM J. Control Optim. 43, 3 (2004), 1063–1077. MR 2114389 | Zbl 1089.49023
[BP2] Bednařík D., Pastor K.: On second-order conditions in unconstrained optimization. Math. Programming, in print; online: Zbl 1211.90276
[BP3] Bednařík D., Pastor K.: Erratum to Elimination of strict convergence in optimization. SIAM J. Control Optim. 45 (2006), 382–387. MR 2225311
[BZ] Ben-Tal A., Zowe J.: Directional derivatives in nonsmooth optimization. J. Optim. Theory Appl. 47 (1985), 483–490. MR 0818873 | Zbl 0556.90074
[CC] Cominetti R., Correa R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28 (1990), 789–809. MR 1051624 | Zbl 0714.49020
[GGR] Ginchev I., Guerraggio A., Rocca M.: From scalar to vector optimization. Appl. Math. 51 (2006), 5–36. MR 2197320 | Zbl 1164.90399
[HSN] Hiriart-Urruty J. B., Strodiot J. J., Nguyen V. H.: Generalized Hessian matrix and second-order optimality conditions for problems with $C^{1,1}$ data. Appl. Math. Optim. 11 (1984), 43–56. MR 0726975
[KT] Klatte D., Tammer K.: On second-order sufficient optimality conditions for $C^{1,1}$ optimization problems. Optimization 19 (1988), 169–179. MR 0948388
[LK] Liu L., Křížek M.: The second order optimality conditions for nonlinear mathematical programming with $C^{1,1}$ data. Appl. Math. 42 (1997), 311–320. MR 1453935
[Q1] Qi L.: Superlinearly convergent approximate Newton methods for $LC^1$ optimization problem. Math. Programming 64 (1994), 277–294. MR 1286451 | Zbl 0820.90102
[Q2] Qi L.: $LC^1$ functions and $LC^1$ optimization. Operations Research and its applications (D.Z. Du, X.S. Zhang and K. Cheng eds.), World Publishing, Beijing, 1996, pp. 4–13. Zbl 1058.68504
[TR] Torre D. L., Rocca M.: Remarks on second order generalized derivatives for differentiable functions with Lipschitzian jacobian. Applied Mathematics E-Notes 3 (2003), 130–137. MR 1995642 | Zbl 1057.49016
[Zo] Zorich V. A.: Mathematical Analysis. : Springer-Verlag, Berlin. 2004.
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