The second order optimality conditions for nonlinear mathematical programming with C 1 , 1 data

Liping Liu; Michal Křížek

Applications of Mathematics (1997)

  • Volume: 42, Issue: 4, page 311-320
  • ISSN: 0862-7940

Abstract

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To find nonlinear minimization problems are considered and standard C 2 -regularity assumptions on the criterion function and constrained functions are reduced to C 1 , 1 -regularity. With the aid of the generalized second order directional derivative for C 1 , 1 real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.

How to cite

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Liu, Liping, and Křížek, Michal. "The second order optimality conditions for nonlinear mathematical programming with $C^{1,1}$ data." Applications of Mathematics 42.4 (1997): 311-320. <http://eudml.org/doc/32984>.

@article{Liu1997,
abstract = {To find nonlinear minimization problems are considered and standard $C^2$-regularity assumptions on the criterion function and constrained functions are reduced to $C^\{1,1\}$-regularity. With the aid of the generalized second order directional derivative for $C^\{1,1\}$ real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.},
author = {Liu, Liping, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {nonlinear programming; constrained problems; $C^\{1;1\}$ functions; second order conditions; constrained optimization; second-order conditions},
language = {eng},
number = {4},
pages = {311-320},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The second order optimality conditions for nonlinear mathematical programming with $C^\{1,1\}$ data},
url = {http://eudml.org/doc/32984},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Liu, Liping
AU - Křížek, Michal
TI - The second order optimality conditions for nonlinear mathematical programming with $C^{1,1}$ data
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 4
SP - 311
EP - 320
AB - To find nonlinear minimization problems are considered and standard $C^2$-regularity assumptions on the criterion function and constrained functions are reduced to $C^{1,1}$-regularity. With the aid of the generalized second order directional derivative for $C^{1,1}$ real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.
LA - eng
KW - nonlinear programming; constrained problems; $C^{1;1}$ functions; second order conditions; constrained optimization; second-order conditions
UR - http://eudml.org/doc/32984
ER -

References

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  13. The second-order conditions of nondominated solutions for C 1 , 1 generalized multiobjective mathematical programming, J. Systems Sci. Math. Sci. 4 (1991), 128–138. (1991) MR1119288
  14. The second order conditions for C 1 , 1 nonlinear mathematical programming, Proc. Prague Math. Conf. 96, Math. Inst., Acad. Sci., Prague, 1996, 153–158. 
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  17. Theory of the Integral, Hafner Pulishing Co., New York, 1937. (1937) Zbl0017.30004

Citations in EuDML Documents

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  1. Liping Liu, Pekka Neittaanmäki, Michal Křížek, Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1 , 1 data
  2. Dušan Bednařík, Karel Pastor, Second-order sufficient condition for ℓ ˜ -stable functions
  3. Ivan Ginchev, Angelo Guerraggio, Matteo Rocca, From scalar to vector optimization
  4. Dušan Bednařík, Karel Pastor, Decrease of property in vector optimization
  5. Karel Pastor, Derivatives of Hadamard type in scalar constrained optimization

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