Displaying similar documents to “Optimality conditions and duality theorems for non-Lipschitz optimization problems.”

A second order η -approximation method for constrained optimization problems involving second order invex functions

Tadeusz Antczak (2009)

Applications of Mathematics

Similarity:

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 η -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order η -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...

Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

Gadhi, N. (2003)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30. In this work, we use the notion of Approximate Hessian introduced by Jeyakumar and Luc [19], and a special scalarization to establish sufficient optimality conditions for constrained multiobjective optimization problems. Throughout this paper, the data are assumed to be of class C^1, but not necessarily of class C^(1.1).

Saddle points criteria via a second order η -approximation approach for nonlinear mathematical programming involving second order invex functions

Tadeusz Antczak (2011)

Kybernetika

Similarity:

In this paper, by using the second order η -approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function η . Moreover, a second order η -saddle point and a second order η -Lagrange function are defined for the so-called second order η -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution...