Geodesic
A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions
Applications of Mathematics, Tome 54 (2009) no. 5, pp. 433-445.

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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.
DOI : 10.1007/s10492-009-0028-2
Classification : 52A01, 90C26, 90C30, 90C46
Keywords: mathematical programming; second order $\eta $-approximated optimization problem; second order invex function; second order optimality conditions 
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Antczak, Tadeusz. A second order $\eta $-approximation method for constrained optimization problems involving second order invex functions. Applications of Mathematics, Tome 54 (2009) no. 5, pp. 433-445. doi : 10.1007/s10492-009-0028-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0028-2/

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