# A second order $\eta $-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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