Second order convexity and a modified objective function method in mathematical programming

• Autorzy: Antczak T.
• Języki publikacji: EN

Abstrakty

EN

An approach to nonlinear constrained mathematical programming problems which makes use of a second order derivative is presented. By using a second order modified objective function method, a modified optimization problem associated with a primal mathematical programming problem is constructed. This auxiliary optimization problem involves a second order approximation of an objective function constituting the primal mathematical programming problem. The equivalence between the original mathematical programming problem and its associated modified optimization problem is established under second order convexity assumption. Several practical O.R. applications show that our method is efficient. Further, an iterative algorithm based on this approach for solving the considered nonlinear mathematical programming problem is given for the case when the functions constituting the problem are second order convex. The convergence theorems for the presented algorithm are established.

Słowa kluczowe

EN

mathematical programming; second order modified objective function optimization problem; second order convex function; second order optimality conditions

PL

programowanie matematyczne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 1
• Strony: 161--182
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Antczak T.

• Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland,

Bibliografia

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