Eigenvalue analysis, subject to boundary conditions

Question

For some non-linear finite element program I have a Tangent stiffness matrix $\textbf{K} \in \mathbb{R}^{n\times n}$, which is symmetric. I want to find the Eigenvector corresponding to the smallest Eigenvalue of this matrix, such that each component of this Eigenvector is non-negative. I know the smallest Eigenpair can be found via different methods (e.g. Inverste iterative method, or Rayleigh quotient iteration, Lanczos method etc.). But, is there a method to extract the smallest Eigenpair of the tangent stiffness matrix, such that all the components of the Eigenvector are non-negative? Is this even possible?