Second order convexity and a modified objective function method in mathematical programming
A second order -approximation method for constrained optimization problems involving second order invex functions
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 -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear...
Saddle points criteria via a second order -approximation approach for nonlinear mathematical programming involving second order invex functions
In this paper, by using the second order -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 . Moreover, a second order -saddle point and a second order -Lagrange function are defined for the so-called second order -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution in the original...
Strict minimizers of order in nonsmooth optimization problems
In the paper, some sufficient optimality conditions for strict minima of order in constrained nonlinear mathematical programming problems involving (locally Lipschitz) -convex functions of order are presented. Furthermore, the concept of strict local minimizer of order is also used to state various duality results in the sense of Mond-Weir and in the sense of Wolfe for such nondifferentiable optimization problems.
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