A second order -approximation method for constrained optimization problems involving second order invex functions
Applications of Mathematics (2009)
- Volume: 54, Issue: 5, page 433-445
- ISSN: 0862-7940
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topAntczak, Tadeusz. "A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions." Applications of Mathematics 54.5 (2009): 433-445. <http://eudml.org/doc/37831>.
@article{Antczak2009,
abstract = {A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $\eta $-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $\eta $-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order $\eta $-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.},
author = {Antczak, Tadeusz},
journal = {Applications of Mathematics},
keywords = {mathematical programming; second order $\eta $-approximated optimization problem; second order invex function; second order optimality conditions; second order -approximated optimization problem; second order invex function; second order optimality conditions},
language = {eng},
number = {5},
pages = {433-445},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions},
url = {http://eudml.org/doc/37831},
volume = {54},
year = {2009},
}
TY - JOUR
AU - Antczak, Tadeusz
TI - A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions
JO - Applications of Mathematics
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 5
SP - 433
EP - 445
AB - A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order $\eta $-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order $\eta $-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order $\eta $-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem.
LA - eng
KW - mathematical programming; second order $\eta $-approximated optimization problem; second order invex function; second order optimality conditions; second order -approximated optimization problem; second order invex function; second order optimality conditions
UR - http://eudml.org/doc/37831
ER -
References
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