<p>This paper is concerned with higher-order optimality conditions for strict minimality in general nonsmooth vector optimization problem with mixed constraints ((GVOPC), for short). Using the higher-order lower and upper set-valued Studniarski derivatives and the higher-order Hadamard differentiability of objective and constraint functions, we establish higher-order necessary optimality conditions for such a problem. Based on these Studniarski derivatives and associated Lagrangian functions, we provide higher-order sufficient optimality conditions for the problem (GVOPC). An application of the result for the twice Fréchet differentiable functions for the second-order strict local efficiency of that problem is presented too. Besides, we provide several methods for checking higher-order sufficient optimality conditions of the problem (GVOPC) using the higher-order lower and upper Studniarski derivatives and Lagrangian functions.</p>