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, Decrease of property in vector optimization
  3. Dušan Bednařík, Karel Pastor, Second-order sufficient condition for ℓ ˜ -stable functions
  4. Ivan Ginchev, Angelo Guerraggio, Matteo Rocca, From scalar to vector optimization
  5. Karel Pastor, Derivatives of Hadamard type in scalar constrained optimization

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