Abstract:In the paper, some sufficient optimality conditions for strict minima of order $m$ in constrained nonlinear mathematical programming problems involving (locally Lipschitz) $(F,\rho )$-convex functions of order $m$ are presented. Furthermore, the concept of strict local minimizer of order $m$ 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.
Keywords: nonsmooth programming, strict local minimizer of order $m$, Clarke's generalized gradient, $(F,\rho )$-convex function of order $m$ with respect to $\theta $
AMS Subject Classification: 90C29, 90C26, 90C46, 49J52