Second-order sufficient condition for ℓ ˜ -stable functions

Dušan Bednařík; Karel Pastor

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2007)

  • Volume: 46, Issue: 1, page 7-18
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Bednařík, Dušan, and Pastor, Karel. "Second-order sufficient condition for $\tilde{\ell }$-stable functions." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 46.1 (2007): 7-18. <http://eudml.org/doc/32457>.

@article{Bednařík2007,
abstract = {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.},
author = {Bednařík, Dušan, Pastor, Karel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {second-order derivative; $C^\{1,1\}$ function; stable function; isolated minimizer of order 2; second-order derivative; function; stable function; isolated minimizer of order 2},
language = {eng},
number = {1},
pages = {7-18},
publisher = {Palacký University Olomouc},
title = {Second-order sufficient condition for $\tilde\{\ell \}$-stable functions},
url = {http://eudml.org/doc/32457},
volume = {46},
year = {2007},
}

TY - JOUR
AU - Bednařík, Dušan
AU - Pastor, Karel
TI - Second-order sufficient condition for $\tilde{\ell }$-stable functions
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2007
PB - Palacký University Olomouc
VL - 46
IS - 1
SP - 7
EP - 18
AB - 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.
LA - eng
KW - second-order derivative; $C^{1,1}$ function; stable function; isolated minimizer of order 2; second-order derivative; function; stable function; isolated minimizer of order 2
UR - http://eudml.org/doc/32457
ER -

References

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  1. Bednařík D., Pastor K., Elimination of strict convergence in optimization, SIAM J. Control Optim. 43, 3 (2004), 1063–1077. Zbl1089.49023MR2114389
  2. Bednařík D., Pastor K., On second-order conditions in unconstrained optimization, Math. Programming, in print; online: http://www.springerlink.com/content/tt7g83q36243l144/ Zbl1211.90276
  3. Bednařík D., Pastor K., Erratum to Elimination of strict convergence in optimization, SIAM J. Control Optim. 45 (2006), 382–387. MR2225311
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  8. Klatte D., Tammer K., On second-order sufficient optimality conditions for C 1 , 1 optimization problems, Optimization 19 (1988), 169–179. (1988) MR0948388
  9. Liu L., Křížek M., The second order optimality conditions for nonlinear mathematical programming with C 1 , 1 data, Appl. Math. 42 (1997), 311–320. (1997) MR1453935
  10. Qi L., Superlinearly convergent approximate Newton methods for L C 1 optimization problem, Math. Programming 64 (1994), 277–294. (1994) Zbl0820.90102MR1286451
  11. Qi L., L C 1 functions and L C 1 optimization, Operations Research and its applications (D.Z. Du, X.S. Zhang and K. Cheng eds.), World Publishing, Beijing, 1996, pp. 4–13. (1996) Zbl1058.68504
  12. 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. Zbl1057.49016MR1995642
  13. Zorich V. A.: Mathematical Analysis., Springer-Verlag, Berlin, , 2004. 

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