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Keywords:
nonsmooth programming; strict local minimizer of order $m$; Clarke's generalized gradient; $(F, \rho )$-convex function of order $m$ with respect to $\theta $
nonsmooth programming; strict local minimizer of order $m$; Clarke's generalized gradient; $(F, \rho )$-convex function of order $m$ with respect to $\theta $
Summary:
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.
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